Nafiz Ishtiaque
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Nafiz Ishtiaque has a total of 16 co-authors. Here are the top co-authors by number of shared publications:
- Yehao Zhou
Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Japan
4 shared publications - Seyed Faroogh Moosavian
Mathematical Institute University of Oxford Woodstock Road OX2 6GG Oxford United Kingdom
3 shared publications - Jaume Gomis
Perimeter Institute for Theoretical Physics N2L 2Y5 Waterloo Ontario Canada
2 shared publications Junya Yagi
Yau Mathematical Sciences Center Tsinghua University 100084 Beijing China
2 shared publications- Saebyeok Jeong
Department of Theoretical Physics CERN 1211 Geneva 23 Switzerland
2 shared publications Seyed Faroogh Moosavian
Department of Physics McGill University H3A 2T8 Montréal QC Canada
2 shared publications
Latest Publications
- 29 August 2026
- Published by Springer Nature in Annales Henri Poincare
- p. 1-85
Refined Invariants and Quantum Curves from Supersymmetric Localization
- 29 August 2026
- Published by Springer Nature in Annales Henri Poincare
- p. 1-85
Refined Invariants and Quantum Curves from Supersymmetric Localization
- 22 July 2025
- Published by Springer Nature in Annales Henri Poincare
- Vol. 27 (6) , 2273-2340
Symmetry Topological Field Theory and Non-Abelian Kramers–Wannier Dualities of Generalised Ising Models
- 22 July 2025
- Published by Springer Nature in Annales Henri Poincare
- Vol. 27 (6) , 2273-2340
Symmetry Topological Field Theory and Non-Abelian Kramers–Wannier Dualities of Generalised Ising Models
- Open Access
- 13 January 2025
- Published by Stichting SciPost in SciPost Physics Core
- Vol. 8 (1) , 003
R-matrices and Miura operators in 5d Chern-Simons theory
We derive Miura operators for W - and Y -algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative \mathfrak{gl}(1) Chern-Simons theory. The expectation value, viewed as the transition amplitude for states in the defect theories forming representations of the affine Yangian of \mathfrak{gl}(1) , satisfies the Yang-Baxter equation and is thus interpreted as an R-matrix. To achieve this, we identify the representations associated with the line and surface defects by calculating the operator product expansions (OPEs) of local operators on the defects, as conditions that anomalous Feynman diagrams cancel each other. We then evaluate the expectation value of the defect intersection using Feynman diagrams. When the line and surface defects are specified, we demonstrate that the expectation value precisely matches the Miura operators and their products.- 13 January 2025
- Published by Stichting SciPost in SciPost Physics Core
- Vol. 8 (1) , 003
Open AccessR-matrices and Miura operators in 5d Chern-Simons theory
We derive Miura operators for W - and Y -algebras from first principles as the expectation value of the intersection between a topological line defect and a holomorphic surface defect in 5-dimensional non-commutative \mathfrak{gl}(1) Chern-Simons theory. The expectation value, viewed as the transition amplitude for states in the defect theories forming representations of the affine Yangian of \mathfrak{gl}(1) , satisfies the Yang-Baxter equation and is thus interpreted as an R-matrix. To achieve this, we identify the representations associated with the line and surface defects by calculating the operator product expansions (OPEs) of local operators on the defects, as conditions that anomalous Feynman diagrams cancel each other. We then evaluate the expectation value of the defect intersection using Feynman diagrams. When the line and surface defects are specified, we demonstrate that the expectation value precisely matches the Miura operators and their products. - Open Access
- 31 October 2024
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 20, 099
Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence
We generalize Aganagic-Okounkov's theory of elliptic stable envelopes, and its physical realization in Dedushenko-Nekrasov's and Bullimore-Zhang's works, to certain varieties without holomorphic symplectic structure or polarization. These classes of varieties include, in particular, classical Higgs branches of 3d $\mathcal N=2$ quiver gauge theories. The Bethe/gauge correspondence relates such a gauge theory to an anisotropic/elliptic superspin chain, and the stable envelopes compute the $R$-matrix that solves the dynamical Yang-Baxter equation (dYBE) for this spin chain. As an illustrative example, we solve the dYBE for the elliptic $\mathfrak{sl}(1|1)$ spin chain with fundamental representations using the corresponding 3d $\mathcal N=2$ SQCD whose classical Higgs branch is the Lascoux resolution of a determinantal variety. Certain Janus partition functions of this theory on $I \times \mathbb E$ for an interval $I$ and an elliptic curve $\mathbb E$ compute the elliptic stable envelopes, and in turn the geometric elliptic $R$-matrix, of the anisotropic $\mathfrak{sl}(1|1)$ spin chain. Furthermore, we consider the 2d and 1d reductions of elliptic stable envelopes and the $R$-matrix. The reduction to 2d gives the K-theoretic stable envelopes and the trigonometric $R$-matrix, and a further reduction to 1d produces the cohomological stable envelopes and the rational $R$-matrix. The latter recovers Rimányi-Rozansky's results that appeared recently in the mathematical literature.- 31 October 2024
- Published by SIGMA (Symmetry, Integrability and Geometry: Methods and Application) in Symmetry, Integrability and Geometry: Methods and Applications
- Vol. 20, 099
Open AccessElliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence
We generalize Aganagic-Okounkov's theory of elliptic stable envelopes, and its physical realization in Dedushenko-Nekrasov's and Bullimore-Zhang's works, to certain varieties without holomorphic symplectic structure or polarization. These classes of varieties include, in particular, classical Higgs branches of 3d $\mathcal N=2$ quiver gauge theories. The Bethe/gauge correspondence relates such a gauge theory to an anisotropic/elliptic superspin chain, and the stable envelopes compute the $R$-matrix that solves the dynamical Yang-Baxter equation (dYBE) for this spin chain. As an illustrative example, we solve the dYBE for the elliptic $\mathfrak{sl}(1|1)$ spin chain with fundamental representations using the corresponding 3d $\mathcal N=2$ SQCD whose classical Higgs branch is the Lascoux resolution of a determinantal variety. Certain Janus partition functions of this theory on $I \times \mathbb E$ for an interval $I$ and an elliptic curve $\mathbb E$ compute the elliptic stable envelopes, and in turn the geometric elliptic $R$-matrix, of the anisotropic $\mathfrak{sl}(1|1)$ spin chain. Furthermore, we consider the 2d and 1d reductions of elliptic stable envelopes and the $R$-matrix. The reduction to 2d gives the K-theoretic stable envelopes and the trigonometric $R$-matrix, and a further reduction to 1d produces the cohomological stable envelopes and the rational $R$-matrix. The latter recovers Rimányi-Rozansky's results that appeared recently in the mathematical literature. - Open Access
- 22 February 2024
- Published by Stichting SciPost in SciPost Physics
- Vol. 16 (2) , 052
Line operators in 4d Chern-Simons theory and Cherkis bows
We show that the phase spaces of a large family of line operators in 4d Chern-Simons theory with GL _n n gauge group are given by Cherkis bow varieties with n n crosses. These line operators are characterized by Hanany-Witten type brane constructions involving D3, D5, and NS5 branes in an \Omega Ω -background. Linking numbers of the five-branes and mass parameters for the D3 brane theories determine the phase spaces and in special cases they correspond to vacuum moduli spaces of 3d \mathcal{N}=4 ???? = 4 quiver theories. Examples include line operators that conjecturally create T, Q, and L-operators in integrable spin chains.
- 22 February 2024
- Published by Stichting SciPost in SciPost Physics
- Vol. 16 (2) , 052
Open AccessLine operators in 4d Chern-Simons theory and Cherkis bows
We show that the phase spaces of a large family of line operators in 4d Chern-Simons theory with GL _n n gauge group are given by Cherkis bow varieties with n n crosses. These line operators are characterized by Hanany-Witten type brane constructions involving D3, D5, and NS5 branes in an \Omega Ω -background. Linking numbers of the five-branes and mass parameters for the D3 brane theories determine the phase spaces and in special cases they correspond to vacuum moduli spaces of 3d \mathcal{N}=4 ???? = 4 quiver theories. Examples include line operators that conjecturally create T, Q, and L-operators in integrable spin chains.
- Open Access
Superspin chains from superstring theory
We present a correspondence between two-dimensional $\mathcal{N} = (2,2)$ supersymmetric gauge theories and rational integrable $\mathfrak{gl}(m|n)$ spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern-Simons theory with gauge group $\mathrm{GL}(m|n)$. The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational $\mathfrak{gl}(m|n)$ spin chains with spins valued in finite-dimensional representations.Open AccessSuperspin chains from superstring theory
We present a correspondence between two-dimensional $\mathcal{N} = (2,2)$ supersymmetric gauge theories and rational integrable $\mathfrak{gl}(m|n)$ spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern-Simons theory with gauge group $\mathrm{GL}(m|n)$. The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational $\mathfrak{gl}(m|n)$ spin chains with spins valued in finite-dimensional representations. - Open Access
- 5 October 2022
- Published by Stichting SciPost in SciPost Physics
- Vol. 13 (4) , 083
Superspin chains from superstring theory
We present a correspondence between two-dimensional \mathcal{N} = (2,2) ???? = ( 2 , 2 ) supersymmetric gauge theories and rational integrable \mathfrak{gl}(m|n) ???? ???? ( m | n ) spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern–Simons theory with gauge group GL(m|n) G L ( m | n ) . The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational \mathfrak{gl}(m|n) ???? ???? ( m | n ) spin chains with spins valued in finite-dimensional representations.
- 5 October 2022
- Published by Stichting SciPost in SciPost Physics
- Vol. 13 (4) , 083
Open AccessSuperspin chains from superstring theory
We present a correspondence between two-dimensional \mathcal{N} = (2,2) ???? = ( 2 , 2 ) supersymmetric gauge theories and rational integrable \mathfrak{gl}(m|n) ???? ???? ( m | n ) spin chains with spin variables taking values in Verma modules. To explain this correspondence, we realize the gauge theories as configurations of branes in string theory and map them by dualities to brane configurations that realize line defects in four-dimensional Chern–Simons theory with gauge group GL(m|n) G L ( m | n ) . The latter configurations embed the superspin chains into superstring theory. We also provide a string theory derivation of a similar correspondence, proposed by Nekrasov, for rational \mathfrak{gl}(m|n) ???? ???? ( m | n ) spin chains with spins valued in finite-dimensional representations.
- Open Access
- 5 August 2020
- Published by Stichting SciPost in SciPost Physics
- Vol. 9 (2) , 017
Topological holography: The example of the D2-D4 brane system
We propose a toy model for holographic duality. The model is constructed by embedding a stack of N N D2-branes and K K D4-branes (with one dimensional intersection) in a 6d topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2d BF theory (resp. 4D Chern-Simons theory) with \mathrm{GL}_N G L N (resp. \mathrm{GL}_K G L K ) gauge group. We propose that in the large N N limit the BF theory on \mathbb{R}^2 ℝ 2 is dual to the closed string theory on \mathbb{R}^2 \times \mathbb{R}_+ \times S^3 ℝ 2 × ℝ + × S 3 with the Chern-Simons defect on \mathbb{R} \times \mathbb{R}_+ \times S^2 ℝ × ℝ + × S 2 . As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection – the algebra is the Yangian of \mathfrak{gl}_K ???? ???? K . We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using D3-D5 brane configuration in type IIB – using supersymmetric twist and \Omega Ω -deformation.
- 5 August 2020
- Published by Stichting SciPost in SciPost Physics
- Vol. 9 (2) , 017
Open AccessTopological holography: The example of the D2-D4 brane system
We propose a toy model for holographic duality. The model is constructed by embedding a stack of N N D2-branes and K K D4-branes (with one dimensional intersection) in a 6d topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2d BF theory (resp. 4D Chern-Simons theory) with \mathrm{GL}_N G L N (resp. \mathrm{GL}_K G L K ) gauge group. We propose that in the large N N limit the BF theory on \mathbb{R}^2 ℝ 2 is dual to the closed string theory on \mathbb{R}^2 \times \mathbb{R}_+ \times S^3 ℝ 2 × ℝ + × S 3 with the Chern-Simons defect on \mathbb{R} \times \mathbb{R}_+ \times S^2 ℝ × ℝ + × S 2 . As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection – the algebra is the Yangian of \mathfrak{gl}_K ???? ???? K . We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using D3-D5 brane configuration in type IIB – using supersymmetric twist and \Omega Ω -deformation.
- Open Access
Topological Holography: The Example of The D2-D4 Brane System
We propose a toy model for holographic duality. The model is constructed by embedding a stack of $N$ D2-branes and $K$ D4-branes (with one dimensional intersection) in a 6D topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2D BF theory (resp. 4D Chern-Simons theory) with $\mathrm{GL}_N$ (resp. $\mathrm{GL}_K$) gauge group. We propose that in the large $N$ limit the BF theory on $\mathbb{R}^2$ is dual to the closed string theory on $\mathbb R^2 \times \mathbb R_+ \times S^3$ with the Chern-Simons defect on $\mathbb R \times \mathbb R_+ \times S^2$. As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection -- the algebra is the Yangian of $\mathfrak{gl}_K$. We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using a D3-D5 brane configuration in type IIB -- using supersymmetric twist and $\Omega$-deformation.Open AccessTopological Holography: The Example of The D2-D4 Brane System
We propose a toy model for holographic duality. The model is constructed by embedding a stack of $N$ D2-branes and $K$ D4-branes (with one dimensional intersection) in a 6D topological string theory. The world-volume theory on the D2-branes (resp. D4-branes) is 2D BF theory (resp. 4D Chern-Simons theory) with $\mathrm{GL}_N$ (resp. $\mathrm{GL}_K$) gauge group. We propose that in the large $N$ limit the BF theory on $\mathbb{R}^2$ is dual to the closed string theory on $\mathbb R^2 \times \mathbb R_+ \times S^3$ with the Chern-Simons defect on $\mathbb R \times \mathbb R_+ \times S^2$. As a check for the duality we compute the operator algebra in the BF theory, along the D2-D4 intersection -- the algebra is the Yangian of $\mathfrak{gl}_K$. We then compute the same algebra, in the guise of a scattering algebra, using Witten diagrams in the Chern-Simons theory. Our computations of the algebras are exact (valid at all loops). Finally, we propose a physical string theory construction of this duality using a D3-D5 brane configuration in type IIB -- using supersymmetric twist and $\Omega$-deformation. - Open Access
- 29 June 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (6) , 1-59
Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals
Bosonic quantum field theories with holomorphic action functionals are realized by two types of constructions involving supersymmetric quantum field theories, compactified on an interval in one type and compactified on a disk and deformed in the other. We establish the equivalence between the two types of constructions by reducing the disk to the interval and the interval to a point. As examples, we discuss constructions of zero-dimensional gauged sigma model, gauged quantum mechanics, gauged symplectic bosons in two dimensions, and Chern-Simons theory and its higher-dimensional variants.
- 29 June 2020
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2020 (6) , 1-59
Open AccessDisk, interval, point: on constructions of quantum field theories with holomorphic action functionals
Bosonic quantum field theories with holomorphic action functionals are realized by two types of constructions involving supersymmetric quantum field theories, compactified on an interval in one type and compactified on a disk and deformed in the other. We establish the equivalence between the two types of constructions by reducing the disk to the interval and the interval to a point. As examples, we discuss constructions of zero-dimensional gauged sigma model, gauged quantum mechanics, gauged symplectic bosons in two dimensions, and Chern-Simons theory and its higher-dimensional variants.