Eric D'Hoker
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Eric D'Hoker has a total of 64 co-authors. Here are the top co-authors by number of shared publications:
- Michael Gutperle
University of California Los Angeles
18 shared publications - Michael B. Green
Department of Applied Mathematics and Theoretical Physics Wilberforce Road CB3 0WA Cambridge UK
13 shared publications - Oliver Schlotterer
Uppsala University
13 shared publications - Christoph F. Uhlemann
Vrije Universiteit Brussel and The International Solvay Institutes
10 shared publications - Boris Pioline
Laboratory of Theoretical and High Energy Physics
8 shared publications - Per Kraus
University of California
8 shared publications
Latest Publications
- Open Access
- 16 July 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (7) , 148
Exact solutions to complex Type IIB supergravity for complex superalgebra F (4) and its real forms
A bstract: We construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra F (4). The geometry is a product of complexified maximally symmetric spaces $$ {\mathcal{M}}_{6\mathbb{C}} $$ and $$ {\mathcal{M}}_{2\mathbb{C}} $$ warped over a complexified surface Σ ℂ . We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter comprise standard Type IIB, Type IIB ⋆ and IIB ′ , as well as theories with 3, 5, 7 and 9 time-like directions. Our classification of real solutions is consistent with and exhausts the real forms of F (4), whose classification we confirm by elementary methods. The geometry of each real form solution is a product of real maximally symmetric spaces $$ {\mathcal{M}}_6 $$ and $$ {\mathcal{M}}_2 $$ warped over a Riemann surface Σ, with various signatures. The real solutions include, among others, known AdS 6 × S 2 × Σ and AdS 2 × S 6 × Σ solutions to standard Type IIB as well as new solutions of the form dS 1,5 × S 2 × Σ in Type IIB ⋆ . There are no real forms of the complex solutions with $$ \mathbf{\mathfrak{so}}\left(7;\mathbb{R}\right) $$ ⨁ $$ \mathbf{\mathfrak{so}}\left(3;\mathbb{R}\right) $$ symmetry. We discuss the relevance of the complex solutions, and of analytic continuations from dS 1,5 × S 2 × Σ to S 6 × S 2 × Σ within complex Type IIB, in connection with holography for the polarized IKKT model.- 16 July 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (7) , 148
Open AccessExact solutions to complex Type IIB supergravity for complex superalgebra F (4) and its real forms
A bstract: We construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra F (4). The geometry is a product of complexified maximally symmetric spaces $$ {\mathcal{M}}_{6\mathbb{C}} $$ and $$ {\mathcal{M}}_{2\mathbb{C}} $$ warped over a complexified surface Σ ℂ . We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter comprise standard Type IIB, Type IIB ⋆ and IIB ′ , as well as theories with 3, 5, 7 and 9 time-like directions. Our classification of real solutions is consistent with and exhausts the real forms of F (4), whose classification we confirm by elementary methods. The geometry of each real form solution is a product of real maximally symmetric spaces $$ {\mathcal{M}}_6 $$ and $$ {\mathcal{M}}_2 $$ warped over a Riemann surface Σ, with various signatures. The real solutions include, among others, known AdS 6 × S 2 × Σ and AdS 2 × S 6 × Σ solutions to standard Type IIB as well as new solutions of the form dS 1,5 × S 2 × Σ in Type IIB ⋆ . There are no real forms of the complex solutions with $$ \mathbf{\mathfrak{so}}\left(7;\mathbb{R}\right) $$ ⨁ $$ \mathbf{\mathfrak{so}}\left(3;\mathbb{R}\right) $$ symmetry. We discuss the relevance of the complex solutions, and of analytic continuations from dS 1,5 × S 2 × Σ to S 6 × S 2 × Σ within complex Type IIB, in connection with holography for the polarized IKKT model. - Open Access
Equivalence of flat connections and Fay identities on arbitrary Riemann surfaces
A flat connection on a Riemann surface with values in an infinite dimensional Lie algebra provides a systematic and effective tool for generating an infinite family of polylogarithms via iterated integrals. The recent literature offers different types of connections, in one or several variables, on compact Riemann surfaces with or without punctures, and in the meromorphic or single-valued categories. In this work, we show that the flatness conditions for the single-valued and modular DHS connection in multiple variables, which was introduced in the companion paper arXiv:2602.01461, are equivalent to the union of all the interchange and Fay identities among DHS integration kernels that were proven in arXiv:2407.11476. Based on the same combinatorial techniques, the flatness conditions on the multivariable Enriquez connection is shown to imply the union of all the interchange and Fay identities for Enriquez kernels.
Open AccessEquivalence of flat connections and Fay identities on arbitrary Riemann surfaces
A flat connection on a Riemann surface with values in an infinite dimensional Lie algebra provides a systematic and effective tool for generating an infinite family of polylogarithms via iterated integrals. The recent literature offers different types of connections, in one or several variables, on compact Riemann surfaces with or without punctures, and in the meromorphic or single-valued categories. In this work, we show that the flatness conditions for the single-valued and modular DHS connection in multiple variables, which was introduced in the companion paper arXiv:2602.01461, are equivalent to the union of all the interchange and Fay identities among DHS integration kernels that were proven in arXiv:2407.11476. Based on the same combinatorial techniques, the flatness conditions on the multivariable Enriquez connection is shown to imply the union of all the interchange and Fay identities for Enriquez kernels.
- Top Cited Papers
- 5 February 2026
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 407 (3) , 43
Relating Flat Connections and Polylogarithms on Higher Genus Riemann Surfaces
- 5 February 2026
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 407 (3) , 43
Top Cited PapersRelating Flat Connections and Polylogarithms on Higher Genus Riemann Surfaces
- Open Access
Single-valued flat connections in several variables on arbitrary Riemann surfaces
Polylogarithms on Riemann surfaces may be constructed efficiently in terms of flat connections that can enjoy various algebraic and analytic properties. In this paper, we present a single-valued and modular invariant connection ${\cal J}_\text{DHS}$ on the configuration space $\text{Cf}_n(Σ)$ of an arbitrary number $n$ of points on an arbitrary compact Riemann surface $Σ$ with or without punctures. The connection ${\cal J}_\text{DHS}$ generalizes an earlier construction for a single variable and is built out of the same integration kernels. We show that ${\cal J}_\text{DHS}$ is flat on $\text{Cf}_n(Σ)$. For the case without punctures, we relate it to the meromorphic multiple-valued Enriquez connection ${\cal K}_\text{E}$ in $n$ variables on the universal cover $\tilde Σ$ of $Σ$ by the composition of a gauge transformation and an automorphism of the Lie algebra in which ${\cal J}_\text{DHS}$ and ${\cal K}_\text{E}$ take values. In a companion paper, we shall establish the equivalence between the flatness of these connections and the corresponding interchange and Fay identities, for arbitrary compact Riemann surfaces.Open AccessSingle-valued flat connections in several variables on arbitrary Riemann surfaces
Polylogarithms on Riemann surfaces may be constructed efficiently in terms of flat connections that can enjoy various algebraic and analytic properties. In this paper, we present a single-valued and modular invariant connection ${\cal J}_\text{DHS}$ on the configuration space $\text{Cf}_n(Σ)$ of an arbitrary number $n$ of points on an arbitrary compact Riemann surface $Σ$ with or without punctures. The connection ${\cal J}_\text{DHS}$ generalizes an earlier construction for a single variable and is built out of the same integration kernels. We show that ${\cal J}_\text{DHS}$ is flat on $\text{Cf}_n(Σ)$. For the case without punctures, we relate it to the meromorphic multiple-valued Enriquez connection ${\cal K}_\text{E}$ in $n$ variables on the universal cover $\tilde Σ$ of $Σ$ by the composition of a gauge transformation and an automorphism of the Lie algebra in which ${\cal J}_\text{DHS}$ and ${\cal K}_\text{E}$ take values. In a companion paper, we shall establish the equivalence between the flatness of these connections and the corresponding interchange and Fay identities, for arbitrary compact Riemann surfaces. - Open Access
- 8 November 2025
- Published by Elsevier in Physics Reports
- Vol. 1158, 1-99
Cascading from N = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD
- 8 November 2025
- Published by Elsevier in Physics Reports
- Vol. 1158, 1-99
Open AccessCascading from N = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD
- Open Access
- 9 October 2025
- Published by Stichting SciPost in SciPost Physics
- Vol. 19 (4) , 091
Worldsheet fermion correlators, modular tensors and higher genus integration kernels
The cyclic product of an arbitrary number of Szegö kernels for even spin structure \delta δ on a compact higher-genus Riemann surface \Sigma Σ may be decomposed via a descent procedure which systematically separates the dependence on the points z_i ∈ \Sigma z i ∈ Σ from the dependence on the spin structure \delta δ . In this paper, we prove two different, but complementary, descent procedures to achieve this decomposition. In the first procedure, the dependence on the points z_i ∈ \Sigma z i ∈ Σ is expressed via the meromorphic multiple-valued Enriquez kernels of e-print 1112.0864 while the dependence on \delta δ resides in multiplets of functions that are independent of z_i z i , locally holomorphic in the moduli of \Sigma Σ and generally do not have simple modular transformation properties. The \delta δ -dependent constants are expressed as multiple convolution integrals over homology cycles of \Sigma Σ , thereby generalizing a similar representation of the individual Enriquez kernels. In the second procedure, which was proposed without proof in e-print 2308.05044, the dependence on z_i z i is expressed in terms the single-valued, modular invariant, but non-meromorphic DHS kernels introduced in e-print 2306.08644 while the dependence on \delta δ resides in modular tensors that are independent of z_i z i and are generally non-holomorphic in the moduli of \Sigma Σ . Although the individual building blocks of these decompositions have markedly different properties, we show that the combinatorial structure of the two decompositions is virtually identical, thereby extending the striking correspondence observed earlier between the roles played by Enriquez and DHS kernels. Both decompositions are further generalized to the case of linear chain products of Szegö kernels.
- 9 October 2025
- Published by Stichting SciPost in SciPost Physics
- Vol. 19 (4) , 091
Open AccessWorldsheet fermion correlators, modular tensors and higher genus integration kernels
The cyclic product of an arbitrary number of Szegö kernels for even spin structure \delta δ on a compact higher-genus Riemann surface \Sigma Σ may be decomposed via a descent procedure which systematically separates the dependence on the points z_i ∈ \Sigma z i ∈ Σ from the dependence on the spin structure \delta δ . In this paper, we prove two different, but complementary, descent procedures to achieve this decomposition. In the first procedure, the dependence on the points z_i ∈ \Sigma z i ∈ Σ is expressed via the meromorphic multiple-valued Enriquez kernels of e-print 1112.0864 while the dependence on \delta δ resides in multiplets of functions that are independent of z_i z i , locally holomorphic in the moduli of \Sigma Σ and generally do not have simple modular transformation properties. The \delta δ -dependent constants are expressed as multiple convolution integrals over homology cycles of \Sigma Σ , thereby generalizing a similar representation of the individual Enriquez kernels. In the second procedure, which was proposed without proof in e-print 2308.05044, the dependence on z_i z i is expressed in terms the single-valued, modular invariant, but non-meromorphic DHS kernels introduced in e-print 2306.08644 while the dependence on \delta δ resides in modular tensors that are independent of z_i z i and are generally non-holomorphic in the moduli of \Sigma Σ . Although the individual building blocks of these decompositions have markedly different properties, we show that the combinatorial structure of the two decompositions is virtually identical, thereby extending the striking correspondence observed earlier between the roles played by Enriquez and DHS kernels. Both decompositions are further generalized to the case of linear chain products of Szegö kernels.
- Open AccessExact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real formsWe construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra $F(4)$. The geometry is a product of complexified maximally symmetric spaces $\mathcal M_{6 {\mathbb C}}$ and $\mathcal M_{2 {\mathbb C}}$ warped over a complexified surface $Σ_{\mathbb C}$. We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter comprise standard Type IIB, Type IIB$^\star$ and IIB$^\prime$, as well as theories with $3$, $5$, $7$ and $9$ time-like directions. Our classification of real solutions is consistent with and exhausts the real forms of $F(4)$, whose classification we confirm by elementary methods. The geometry of each real form solution is a product of real maximally symmetric spaces $\mathcal M_6$ and $\mathcal M_2$ warped over a Riemann surface $Σ$, with various signatures. The real solutions include, among others, known $AdS_6 \times S^2 \times Σ$ and $AdS_2 \times S^6 \times Σ$ solutions to standard Type IIB as well as new solutions of the form $dS_{1,5}\times S^2 \times Σ$ in Type IIB$^\star$. There are no real forms of the complex solutions with $\mathfrak{so} (7;{\mathbb R}) \oplus \mathfrak{so} (3;{\mathbb R})$ symmetry. We discuss the relevance of the complex solutions, and of analytic continuations from $dS_{1,5}\times S^2\timesΣ$ to $S^6\times S^2\timesΣ$ within complex Type IIB, in connection with holography for the polarized IKKT model.Open AccessExact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real formsWe construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra $F(4)$. The geometry is a product of complexified maximally symmetric spaces $\mathcal M_{6 {\mathbb C}}$ and $\mathcal M_{2 {\mathbb C}}$ warped over a complexified surface $Σ_{\mathbb C}$. We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter comprise standard Type IIB, Type IIB$^\star$ and IIB$^\prime$, as well as theories with $3$, $5$, $7$ and $9$ time-like directions. Our classification of real solutions is consistent with and exhausts the real forms of $F(4)$, whose classification we confirm by elementary methods. The geometry of each real form solution is a product of real maximally symmetric spaces $\mathcal M_6$ and $\mathcal M_2$ warped over a Riemann surface $Σ$, with various signatures. The real solutions include, among others, known $AdS_6 \times S^2 \times Σ$ and $AdS_2 \times S^6 \times Σ$ solutions to standard Type IIB as well as new solutions of the form $dS_{1,5}\times S^2 \times Σ$ in Type IIB$^\star$. There are no real forms of the complex solutions with $\mathfrak{so} (7;{\mathbb R}) \oplus \mathfrak{so} (3;{\mathbb R})$ symmetry. We discuss the relevance of the complex solutions, and of analytic continuations from $dS_{1,5}\times S^2\timesΣ$ to $S^6\times S^2\timesΣ$ within complex Type IIB, in connection with holography for the polarized IKKT model.
- Open Access
- 13 June 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (6) , 1-48
Approaching Argyres-Douglas theories
The Seiberg-Witten solution to four-dimensional $$ \mathcal{N} $$ = 2 super-Yang-Mills theory with gauge group SU(N) and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$ . A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the ℤ 2N symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for SU(3). The intrinsic periods and Kähler potential of the $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$ superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kähler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions ∆ > 1 acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to ∆ ≤ 1 operators spoils the positivity and convexity of the intrinsic Kähler potential.- 13 June 2024
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2024 (6) , 1-48
Open AccessApproaching Argyres-Douglas theories
The Seiberg-Witten solution to four-dimensional $$ \mathcal{N} $$ = 2 super-Yang-Mills theory with gauge group SU(N) and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$ . A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the ℤ 2N symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for SU(3). The intrinsic periods and Kähler potential of the $$ \left({\mathfrak{a}}_1,{\mathfrak{a}}_{N-1}\right) $$ superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kähler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions ∆ > 1 acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to ∆ ≤ 1 operators spoils the positivity and convexity of the intrinsic Kähler potential. - Open Access
Approaching Argyres-Douglas theories
The Seiberg-Witten solution to four-dimensional $\mathcal{N}=2$ super-Yang-Mills theory with gauge group $\text{SU}(N)$ and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type $(\mathfrak{a}_1,\mathfrak{a}_{N-1})$. A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the $\mathbb{Z}_{2N}$ symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for $\text{SU}(3)$. The intrinsic periods and Kähler potential of the $(\mathfrak{a}_1,\mathfrak{a}_{N-1})$ superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kähler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions $Δ>1$ acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to $Δ\leq 1$ operators spoils the positivity and convexity of the intrinsic Kähler potential.Open AccessApproaching Argyres-Douglas theories
The Seiberg-Witten solution to four-dimensional $\mathcal{N}=2$ super-Yang-Mills theory with gauge group $\text{SU}(N)$ and without hypermultiplets is used to investigate the neighborhood of the maximal Argyres-Douglas points of type $(\mathfrak{a}_1,\mathfrak{a}_{N-1})$. A convergent series expansion for the Seiberg-Witten periods near the Argyres-Douglas points is obtained by analytic continuation of the series expansion around the $\mathbb{Z}_{2N}$ symmetric point derived in arXiv:2208.11502. Along with direct integration of the Picard-Fuchs equations for the periods, the expansion is used to determine the location of the walls of marginal stability for $\text{SU}(3)$. The intrinsic periods and Kähler potential of the $(\mathfrak{a}_1,\mathfrak{a}_{N-1})$ superconformal fixed point are computed by letting the strong coupling scale tend to infinity. We conjecture that the resulting intrinsic Kähler potential is positive definite and convex, with a unique minimum at the Argyres-Douglas point, provided only intrinsic Coulomb branch operators with unitary scaling dimensions $Δ>1$ acquire a vacuum expectation value, and provide both analytical and numerical evidence in support of this conjecture. In all the low rank examples considered here, it is found that turning on moduli dual to $Δ\leq 1$ operators spoils the positivity and convexity of the intrinsic Kähler potential. - Open Access
Cyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this paper we discover that, for Riemann surfaces of genus two and even spin structures, a collection of novel identities leads to a dramatic simplification of the spin structure sum. Explicit formulas for an arbitrary number of vertex points are obtained in two steps. First, we show that the spin structure dependence of a cyclic product of Szeg\"o kernels (i.e. Dirac propagators for worldsheet fermions) may be reduced to the spin structure dependence of the four-point function. Of particular importance are certain trilinear relations that we shall define and prove. In a second step, the known expressions for the genus-two even spin structure measure are used to perform the remaining spin structure sums. The dependence of the spin summand on the vertex points is reduced to simple building blocks that can already be identified from the two-point function. The hyper-elliptic formulation of genus-two Riemann surfaces is used to derive these results, and its $SL(2,\mathbb C)$ covariance is employed to organize the calculations and the structure of the final formulas. The translation of these results into the language of Riemann $\vartheta$-functions, and applications to the evaluation of higher-point string amplitudes, are relegated to subsequent companion papers.Open AccessCyclic products of Szegö kernels and spin structure sums I: hyper-elliptic formulation
The summation over spin structures, which is required to implement the GSO projection in the RNS formulation of superstring theories, often presents a significant impediment to the explicit evaluation of superstring amplitudes. In this paper we discover that, for Riemann surfaces of genus two and even spin structures, a collection of novel identities leads to a dramatic simplification of the spin structure sum. Explicit formulas for an arbitrary number of vertex points are obtained in two steps. First, we show that the spin structure dependence of a cyclic product of Szeg\"o kernels (i.e. Dirac propagators for worldsheet fermions) may be reduced to the spin structure dependence of the four-point function. Of particular importance are certain trilinear relations that we shall define and prove. In a second step, the known expressions for the genus-two even spin structure measure are used to perform the remaining spin structure sums. The dependence of the spin summand on the vertex points is reduced to simple building blocks that can already be identified from the two-point function. The hyper-elliptic formulation of genus-two Riemann surfaces is used to derive these results, and its $SL(2,\mathbb C)$ covariance is employed to organize the calculations and the structure of the final formulas. The translation of these results into the language of Riemann $\vartheta$-functions, and applications to the evaluation of higher-point string amplitudes, are relegated to subsequent companion papers.