Indranil Halder
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Indranil Halder has a total of 12 co-authors. Here are the top co-authors by number of shared publications:
- Shiraz Minwalla
Tata Institute of Fundamental Research
9 shared publications - Anshuman Dey
Department of Theoretical Physics Tata Institute of Fundamental Research Homi Bhabha Rd 400005 Mumbai India
6 shared publications - Naveen S. Prabhakar
International Centre for Theoretical Sciences Tata Institute of Fundamental Research 560089 Shivakote Bengaluru India
5 shared publications - Sachin Jain
Department of Physics, Indian Institute of Science Education and Research, Pune, India
5 shared publications - Lavneet Janagal
Department of Theoretical Physics Tata Institute of Fundamental Research Homi Bhabha Rd 400005 Mumbai India
4 shared publications - Lavneet Janagal
School of Physics Korea Institute for Advanced Studies 02455 Seoul South Korea
2 shared publications
Latest Publications
- Open Access
- 19 February 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (2) , 1-170
Classifying and constraining local four photon and four graviton S-matrices
We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants s, t and u. We construct these modules for every value of the spacetime dimension D, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by s2 at fixed t. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for D ≤ 6. For D ≥ 7 there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for D ≤ 6. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also violates our conjectured Regge growth bound, at least when D ≤ 6, even when the exchanged particles have low spin.
- 19 February 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (2) , 1-170
Open AccessClassifying and constraining local four photon and four graviton S-matrices
We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants s, t and u. We construct these modules for every value of the spacetime dimension D, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by s2 at fixed t. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for D ≤ 6. For D ≥ 7 there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for D ≤ 6. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also violates our conjectured Regge growth bound, at least when D ≤ 6, even when the exchanged particles have low spin.
- Open Access
- 20 November 2019
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2019 (11) , 113
The large N phase diagram of $ \mathcal{N} $ = 2 SU(N) Chern-Simons theory with one fundamental chiral multipletWe study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large N limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the ’t Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large N $$ \mathcal{N} $$ = 2 supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general $$ \mathcal{N} $$ = 1 supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an SU(N ) Chern-Simons gauge field, at arbitrary values of the ’t Hooft coupling.- 20 November 2019
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2019 (11) , 113
Open AccessThe large N phase diagram of $ \mathcal{N} $ = 2 SU(N) Chern-Simons theory with one fundamental chiral multipletWe study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large N limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the ’t Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large N $$ \mathcal{N} $$ = 2 supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general $$ \mathcal{N} $$ = 1 supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an SU(N ) Chern-Simons gauge field, at arbitrary values of the ’t Hooft coupling. - Open Access
Classifying and constraining local four photon and four graviton S-matrices
We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants $s$, $t$ and $u$. We construct these modules for every value of the spacetime dimension $D$, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by $s^2$ at fixed $t$. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for $D \leq 6$. For $D \geq 7$ there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for $D\leq 6$. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also such violates our conjectured Regge growth bound, at least when $D\leq 6$, even when the exchanged particles have low spin.Open AccessClassifying and constraining local four photon and four graviton S-matrices
We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants $s$, $t$ and $u$. We construct these modules for every value of the spacetime dimension $D$, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by $s^2$ at fixed $t$. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for $D \leq 6$. For $D \geq 7$ there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for $D\leq 6$. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also such violates our conjectured Regge growth bound, at least when $D\leq 6$, even when the exchanged particles have low spin. - Open Access
- 15 November 2019
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2019 (11) , 89
Matter Chern Simons theories in a background magnetic field
We study large N 2+1 dimensional fermions in the fundamental representation of an SU(N)k Chern Simons gauge group in the presence of a uniform background magnetic field for the U (1) global symmetry of this theory. The magnetic field modifies the Schwinger Dyson equation for the propagator in an interesting way; the product between the self energy and the Greens function is replaced by a Moyal star product. Employing a basis of functions previously used in the study of non-commutative solitons, we are able to exactly solve the Schwinger Dyson equation and so determine the fermion propagator. The propagator has a series of poles (and no other singularities) whose locations yield a spectrum of single particle energies at arbitrary t’ Hooft coupling and chemical potential. The usual free fermion Landau levels spectrum is shifted and broadened out; we compute the shifts and widths of these levels at arbitrary t’Hooft coupling. As a check on our results we independently solve for the propagators of the conjecturally dual theory of Chern Simons gauged large N fundamental Wilson Fisher bosons also in a background magnetic field but this time only at zero chemical potential. The spectrum of single particle states of the bosonic theory precisely agrees with those of the fermionic theory under Bose-Fermi duality.
- 15 November 2019
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2019 (11) , 89
Open AccessMatter Chern Simons theories in a background magnetic field
We study large N 2+1 dimensional fermions in the fundamental representation of an SU(N)k Chern Simons gauge group in the presence of a uniform background magnetic field for the U (1) global symmetry of this theory. The magnetic field modifies the Schwinger Dyson equation for the propagator in an interesting way; the product between the self energy and the Greens function is replaced by a Moyal star product. Employing a basis of functions previously used in the study of non-commutative solitons, we are able to exactly solve the Schwinger Dyson equation and so determine the fermion propagator. The propagator has a series of poles (and no other singularities) whose locations yield a spectrum of single particle energies at arbitrary t’ Hooft coupling and chemical potential. The usual free fermion Landau levels spectrum is shifted and broadened out; we compute the shifts and widths of these levels at arbitrary t’Hooft coupling. As a check on our results we independently solve for the propagators of the conjecturally dual theory of Chern Simons gauged large N fundamental Wilson Fisher bosons also in a background magnetic field but this time only at zero chemical potential. The spectrum of single particle states of the bosonic theory precisely agrees with those of the fermionic theory under Bose-Fermi duality.
- Open AccessThe large $N$ phase diagram of ${\cal N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multipletWe study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large $N$ limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the 't Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large $N$ ${\cal N}=2$ supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general ${\cal N} = 1$ supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an $SU(N)$ Chern-Simons gauge field, at arbitrary values of the 't Hooft coupling.Open AccessThe large $N$ phase diagram of ${\cal N}=2$ $SU(N)$ Chern-Simons theory with one fundamental chiral multipletWe study the theory of a single fundamental fermion and boson coupled to Chern-Simons theory at leading order in the large $N$ limit. Utilizing recent progress in understanding the Higgsed phase in Chern-Simons-Matter theories, we compute the quantum effective potential that is exact to all orders in the 't Hooft coupling for the lightest scalar operator of this theory at finite temperature. Specializing to the zero temperature limit we use this potential to determine the phase diagram of the large $N$ ${\cal N}=2$ supersymmetric theory with this field content. This intricate two dimensional phase diagram has four topological phases that are separated by lines of first and second order phase transitions and includes special conformal points at which the infrared dynamics is governed by Chern-Simons theory coupled respectively to free bosons, Gross-Neveu fermions, and to a theory of Wilson-Fisher bosons plus free fermions. We also describe the vacuum structure of the most general ${\cal N} = 1$ supersymmetric theory with one fundamental boson and one fundamental fermion coupled to an $SU(N)$ Chern-Simons gauge field, at arbitrary values of the 't Hooft coupling.
- Open Access
Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
It has been conjectured that Chern-Simons (CS) gauged `regular' bosons in the fundamental representation are `level-rank' dual to CS gauged critical fermions also in the fundamental representation. Generic relevant deformations of these conformal field theories lead to one of two distinct massive phases. In previous work, the large $N$ thermal free energy for the bosonic theory in the unHiggsed phase has been demonstrated to match the corresponding fermionic results under duality. In this note we evaluate the large $N$ thermal free energy of the bosonic theory in the Higgsed phase and demonstrate that our results, again, perfectly match the predictions of duality. Our computation is performed in a unitary gauge by integrating out the physical excitations of the theory - i.e. W bosons - at all orders in the 't Hooft coupling. Our results allow us to construct an exact quantum effective potential for ${\bar \phi} \phi$, the lightest gauge invariant scalar operator in the theory. In the zero temperature limit this exact Landau-Ginzburg potential is non-analytic at ${\bar \phi \phi}=0$. The extrema of this effective potential at positive ${\bar \phi}\phi$ solve the gap equations in the Higgsed phase while the extrema at negative ${\bar \phi} \phi$ solve the gap equations in the unHiggsed phase. Our effective potential is bounded from below only for a certain range of $x_6$ (the parameter that governs sextic interactions of $\phi$). This observation suggests that the regular boson theory has a stable vacuum only when $x_6$ lies in this range.Open AccessDuality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
It has been conjectured that Chern-Simons (CS) gauged `regular' bosons in the fundamental representation are `level-rank' dual to CS gauged critical fermions also in the fundamental representation. Generic relevant deformations of these conformal field theories lead to one of two distinct massive phases. In previous work, the large $N$ thermal free energy for the bosonic theory in the unHiggsed phase has been demonstrated to match the corresponding fermionic results under duality. In this note we evaluate the large $N$ thermal free energy of the bosonic theory in the Higgsed phase and demonstrate that our results, again, perfectly match the predictions of duality. Our computation is performed in a unitary gauge by integrating out the physical excitations of the theory - i.e. W bosons - at all orders in the 't Hooft coupling. Our results allow us to construct an exact quantum effective potential for ${\bar \phi} \phi$, the lightest gauge invariant scalar operator in the theory. In the zero temperature limit this exact Landau-Ginzburg potential is non-analytic at ${\bar \phi \phi}=0$. The extrema of this effective potential at positive ${\bar \phi}\phi$ solve the gap equations in the Higgsed phase while the extrema at negative ${\bar \phi} \phi$ solve the gap equations in the unHiggsed phase. Our effective potential is bounded from below only for a certain range of $x_6$ (the parameter that governs sextic interactions of $\phi$). This observation suggests that the regular boson theory has a stable vacuum only when $x_6$ lies in this range. - Open Access
- 6 November 2018
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2018 (11) , 20
Duality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
A bstract: It has been conjectured that Chern-Simons (CS) gauged ‘regular’ bosons in the fundamental representation are ‘level-rank’ dual to CS gauged critical fermions also in the fundamental representation. Generic relevant deformations of these conformal field theories lead to one of two distinct massive phases. In previous work, the large N thermal free energy for the bosonic theory in the unHiggsed phase has been demonstrated to match the corresponding fermionic results under duality. In this note we evaluate the large N thermal free energy of the bosonic theory in the Higgsed phase and demonstrate that our results, again, perfectly match the predictions of duality. Our computation is performed in a unitary gauge by integrating out the physical excitations of the theory — i.e. W bosons — at all orders in the ’t Hooft coupling. Our results allow us to construct an exact quantum effective potential for $$ \overline{\phi}\phi $$ , the lightest gauge invariant scalar operator in the theory. In the zero temperature limit this exact Landau-Ginzburg potential is non-analytic at $$ \overline{\phi}\phi $$ = 0. The extrema of this effective potential at positive $$ \overline{\phi}\phi $$ solve the gap equations in the Higgsed phase while the extrema at negative $$ \overline{\phi}\phi $$ solve the gap equations in the unHiggsed phase. Our effective potential is bounded from below only for a certain range of x 6 (the parameter that governs sextic interactions of ϕ ). This observation suggests that the regular boson theory has a stable vacuum only when x 6 lies in this range.- 6 November 2018
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2018 (11) , 20
Open AccessDuality and an exact Landau-Ginzburg potential for quasi-bosonic Chern-Simons-Matter theories
A bstract: It has been conjectured that Chern-Simons (CS) gauged ‘regular’ bosons in the fundamental representation are ‘level-rank’ dual to CS gauged critical fermions also in the fundamental representation. Generic relevant deformations of these conformal field theories lead to one of two distinct massive phases. In previous work, the large N thermal free energy for the bosonic theory in the unHiggsed phase has been demonstrated to match the corresponding fermionic results under duality. In this note we evaluate the large N thermal free energy of the bosonic theory in the Higgsed phase and demonstrate that our results, again, perfectly match the predictions of duality. Our computation is performed in a unitary gauge by integrating out the physical excitations of the theory — i.e. W bosons — at all orders in the ’t Hooft coupling. Our results allow us to construct an exact quantum effective potential for $$ \overline{\phi}\phi $$ , the lightest gauge invariant scalar operator in the theory. In the zero temperature limit this exact Landau-Ginzburg potential is non-analytic at $$ \overline{\phi}\phi $$ = 0. The extrema of this effective potential at positive $$ \overline{\phi}\phi $$ solve the gap equations in the Higgsed phase while the extrema at negative $$ \overline{\phi}\phi $$ solve the gap equations in the unHiggsed phase. Our effective potential is bounded from below only for a certain range of x 6 (the parameter that governs sextic interactions of ϕ ). This observation suggests that the regular boson theory has a stable vacuum only when x 6 lies in this range. - Open Access
Bose-Fermi Chern-Simons Dualities in the Higgsed Phase
It has been conjectured that fermions minimally coupled to a Chern-Simons gauge field define a conformal field theory (CFT) that is level-rank dual to Chern-Simons gauged Wilson-Fisher Bosons. The CFTs in question admit relevant deformations parametrized by a real mass. When the mass deformation is positive, the duality of the two deformed theories has previously been checked in detail in the large $N$ limit by comparing explicit all orders results on both sides of the duality. In this paper we perform a similar check for the case of negative mass deformations. In this case the bosonic field condenses triggering the Higgs mechanism. The effective excitations in this phase are massive $W$ bosons. By summing all leading large $N$ graphs involving these $W$ bosons we find an all orders (in the 't Hooft coupling) result for the thermal free energy of the bosonic theory in the condensed phase. Our final answer perfectly matches the previously obtained fermionic free energy under the conjectured duality map.Open AccessBose-Fermi Chern-Simons Dualities in the Higgsed Phase
It has been conjectured that fermions minimally coupled to a Chern-Simons gauge field define a conformal field theory (CFT) that is level-rank dual to Chern-Simons gauged Wilson-Fisher Bosons. The CFTs in question admit relevant deformations parametrized by a real mass. When the mass deformation is positive, the duality of the two deformed theories has previously been checked in detail in the large $N$ limit by comparing explicit all orders results on both sides of the duality. In this paper we perform a similar check for the case of negative mass deformations. In this case the bosonic field condenses triggering the Higgs mechanism. The effective excitations in this phase are massive $W$ bosons. By summing all leading large $N$ graphs involving these $W$ bosons we find an all orders (in the 't Hooft coupling) result for the thermal free energy of the bosonic theory in the condensed phase. Our final answer perfectly matches the previously obtained fermionic free energy under the conjectured duality map. - Open AccessNotes on Melonic $O(N)^{q-1}$ Tensor ModelsIt has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group $O(N)^{q-1}$ agrees with the large $N$ limit of the SYK model. In these notes we investigate aspects of the dynamics of the $O(N)^{q-1}$ theories that differ from their SYK counterparts. We argue that the spectrum of fluctuations about the finite temperature saddle point in these theories has $(q-1)\frac{N^2}{2}$ new light modes in addition to the light Schwarzian mode that exists even in the SYK model, suggesting that the bulk dual description of theories differ significantly if they both exist. We also study the thermal partition function of a mass deformed version of the SYK model. At large mass we show that the effective entropy of this theory grows with energy like $E \ln E$ (i.e. faster than Hagedorn) up to energies of order $N^2$. The canonical partition function of the model displays a deconfinement or Hawking Page type phase transition at temperatures of order $1/\ln N$. We derive these results in the large mass limit but argue that they are qualitatively robust to small corrections in $J/m$.Open AccessNotes on Melonic $O(N)^{q-1}$ Tensor ModelsIt has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group $O(N)^{q-1}$ agrees with the large $N$ limit of the SYK model. In these notes we investigate aspects of the dynamics of the $O(N)^{q-1}$ theories that differ from their SYK counterparts. We argue that the spectrum of fluctuations about the finite temperature saddle point in these theories has $(q-1)\frac{N^2}{2}$ new light modes in addition to the light Schwarzian mode that exists even in the SYK model, suggesting that the bulk dual description of theories differ significantly if they both exist. We also study the thermal partition function of a mass deformed version of the SYK model. At large mass we show that the effective entropy of this theory grows with energy like $E \ln E$ (i.e. faster than Hagedorn) up to energies of order $N^2$. The canonical partition function of the model displays a deconfinement or Hawking Page type phase transition at temperatures of order $1/\ln N$. We derive these results in the large mass limit but argue that they are qualitatively robust to small corrections in $J/m$.