About

Eric D'Hoker is a Distinguished Research Professor in the Department of Physics & Astronomy at UCLA. His research interests are in quantum field theory and string theory, with applications to particle physics, and occasionally to condensed matter physics and mathematics. He holds a Ph.D. from Princeton University, obtained in 1981, and a B.Sc. from Ecole Polytechnique in France, earned in 1978. Dr. D'Hoker is a member of the Mani L. Bhaumik Institute for Theoretical Physics, an Honorary Trustee of the Aspen Center for Physics, and serves as an associate editor of the journals JHEP and SIGMA. His professional activities include contributing to the academic community through research, editorial work, and participation in various institutional roles.

Selected publications

• Relating Flat Connections and Polylogarithms on Higher Genus Riemann Surfaces

  Communications in Mathematical Physics · 2026-02-05 · 2 citations

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• Worldsheet fermion correlators, modular tensors and higher genus integration kernels

  SciPost Physics · 2025-10-09 · 3 citations

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  The cyclic product of an arbitrary number of Szegö kernels for even spin structure \delta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>δ</mml:mi> </mml:math> on a compact higher-genus Riemann surface \Sigma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Σ</mml:mi> </mml:math> may be decomposed via a descent procedure which systematically separates the dependence on the points z_i ∈ \Sigma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>z</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mi>Σ</mml:mi> </mml:mrow> </mml:math> from the dependence on the spin structure \delta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>δ</mml:mi> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mi>z</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo>∈</mml:mo> <mml:mi>Σ</mml:mi> </mml:mrow> </mml:math> is expressed via the meromorphic multiple-valued Enriquez kernels of e-print 1112.0864 while the dependence on \delta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>δ</mml:mi> </mml:math> resides in multiplets of functions that are independent of z_i <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>z</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> , locally holomorphic in the moduli of \Sigma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Σ</mml:mi> </mml:math> and generally do not have simple modular transformation properties. The \delta <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>δ</mml:mi> </mml:math> -dependent constants are expressed as multiple convolution integrals over homology cycles of \Sigma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Σ</mml:mi> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>z</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>δ</mml:mi> </mml:math> resides in modular tensors that are independent of z_i <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>z</mml:mi> <mml:mi>i</mml:mi> </mml:msub> </mml:math> and are generally non-holomorphic in the moduli of \Sigma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>Σ</mml:mi> </mml:math> . 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.

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• Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms

  ArXiv.org · 2025-08-20

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  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 $Σ_{\mathbb C}$. 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.

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• Cascading from  <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e5624" altimg="si24.svg"> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo linebreak="goodbreak" linebreakstyle="after">=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

  Physics Reports · 2025-11-08 · 2 citations

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• Meromorphic higher-genus integration kernels via convolution over homology cycles

  arXiv (Cornell University) · 2025-02-20 · 1 citations

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  Polylogarithms on arbitrary higher-genus Riemann surfaces can be constructed from meromorphic integration kernels with at most simple poles, whose definition was given by Enriquez via functional properties. In this work, homotopy-invariant convolution integrals over homology cycles are shown to provide a direct construction of Enriquez kernels solely from holomorphic Abelian differentials and the prime form. Our new representation is used to demonstrate the closure of the space of Enriquez kernels under convolution over homology cycles and under variations of the moduli. The results of this work further strengthen the remarkable parallels of Enriquez kernels with the non-holomorphic modular tensors recently developed in an alternative construction of higher-genus polylogarithms.

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• Meromorphic higher-genus integration kernels via convolution over homology cycles

  Journal of Physics A Mathematical and Theoretical · 2025-08-04 · 5 citations

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  Abstract Polylogarithms on arbitrary higher-genus Riemann surfaces can be constructed from meromorphic integration kernels with at most simple poles, whose definition was given by Enriquez via functional properties. In this work, homotopy-invariant convolution integrals over homology cycles are shown to provide a direct construction of Enriquez kernels solely from holomorphic Abelian differentials and the prime form. Our new representation is used to demonstrate the closure of the space of Enriquez kernels under convolution over homology cycles and under variations of the moduli. The results of this work further strengthen the remarkable parallels of Enriquez kernels with the non-holomorphic modular tensors recently developed in an alternative construction of higher-genus polylogarithms.

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• Relating flat connections and polylogarithms on higher genus Riemann surfaces

  Open MIND · 2025-01-13 · 2 citations

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  In this work, we relate two recent constructions that generalize classical (genus-zero) polylogarithms to higher-genus Riemann surfaces. A flat connection valued in a freely generated Lie algebra on a punctured Riemann surface of arbitrary genus produces an infinite family of homotopy-invariant iterated integrals associated to all possible words in the alphabet of the Lie algebra generators. Each iterated integral associated to a word is a higher-genus polylogarithm. Different flat connections taking values in the same Lie algebra on a given Riemann surface may be related to one another by the composition of a gauge transformation and an automorphism of the Lie algebra, thus producing closely related families of polylogarithms. In this paper we provide two methods to explicitly construct this correspondence between the meromorphic multiple-valued connection introduced by Enriquez in e-Print 1112.0864 and the non-meromorphic single-valued and modular-invariant connection introduced by D'Hoker, Hidding and Schlotterer, in e-Print 2306.08644.

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• Constructing polylogarithms on higher-genus Riemann surfaces

  Communications in Number Theory and Physics · 2025-01-01 · 14 citations

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• Cyclic Products of Higher-Genus Szegö Kernels, Modular Tensors, and Polylogarithms

  Physical Review Letters · 2024-07-09 · 9 citations

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  A wealth of information on multiloop string amplitudes is encoded in fermionic two-point functions known as Szegö kernels. Here we show that cyclic products of any number of Szegö kernels on a Riemann surface of arbitrary genus may be decomposed into linear combinations of modular tensors on moduli space that carry all the dependence on the spin structure δ. The δ-independent coefficients in these combinations carry all the dependence on the marked points and are composed of the integration kernels of higher-genus polylogarithms. We determine the antiholomorphic moduli derivatives of the δ-dependent modular tensors.

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• Cascading from $\mathscr{N}=2$ Supersymmetric Yang-Mills Theory to Confinement and Chiral Symmetry Breaking in Adjoint QCD

  arXiv (Cornell University) · 2024-12-29 · 1 citations

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  We argue that adjoint QCD in 3+1 dimensions, with any $SU(N)$ gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}=2$ SUSY Yang-Mills theory with the same gauge group, by giving a SUSY-breaking mass $M$ to the scalars in the $\mathscr{N} = 2$ vector multiplet. This flow can be analyzed rigorously at small $M$, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}=2$ Coulomb branch. The analysis can be extended to all $M$ using an Abelian dual description that arises from the $N$ multi-monopole points of the $\mathscr{N} = 2$ theory. At each such point, there are $N-1$ hypermultiplet Higgs fields $h_m^{i = 1, 2}$, which are $SU(2)_R$ doublets. We provide a detailed study of the phase diagram as a function of $M$, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields $h_m^i$ successively turn on, and which interpolates between the Coulomb branch at small $M$, where all $h_m^i = 0$, and a maximal Higgs branch, where all $h_m^i \neq 0$, at sufficiently large $M$. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-$N$ scaling of various observables. The spontaneous breaking pattern $SU(2)_R \to U(1)_R$, consistent with the Vafa-Witten theorem, is ensured by an intricate alignment mechanism for the $h_m^i$ in the dual, and leads to a $\mathbb{C}\mathbb{P}^1$ sigma model of increasing radius along the cascade.

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Awards & honors

• Mani L. Bhaumik Institute for Theoretical Physics