Publications

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• Four lectures on Euler integrals

  Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera, Simon Telen

  SciPost Phys. Lect. Notes 75 (2023) · published 26 October 2023 | Toggle abstract · pdf

  These lecture notes provide a self-contained introduction to Euler integrals, which are frequently encountered in applications. In particle physics, they arise as Feynman integrals or string amplitudes. Our four selected topics demonstrate the diverse mathematical techniques involved in the study of Euler integrals, including polyhedral geometry, very affine varieties, differential equations, and computational algebra.

  4 citations

• Exact entanglement in the driven quantum symmetric simple exclusion process

  Denis Bernard, Ludwig Hruza

  SciPost Phys. 15, 175 (2023) · published 20 October 2023 | Toggle abstract · pdf

  Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We confirm this observation by studying a suitable toy model for mesoscopic transport: the open quantum symmetric simple exclusion process (QSSEP). We derive exact formulae for its mutual information between different subsystems in the steady state and show that it satisfies a volume law. Surprisingly, the QSSEP entanglement properties only depend on data related to its transport properties and we suspect that such a relation might hold for more general mesoscopic systems. Exploiting the free probability structure of QSSEP, we obtain these results by developing a new method to determine the eigenvalue spectrum of sub-blocks of random matrices from their so-called local free cumulants - a mathematical result on its own with potential applications in the theory of random matrices. As an illustration of this method, we show how to compute expectation values of observables in systems satisfying the Eigenstate Thermalization Hypothesis (ETH) from the local free cumulants.

  8 citations

• Matrix product operator representations for the local conserved quantities of the Heisenberg chain

  Kyoichi Yamada, Kohei Fukai

  SciPost Phys. Core 6, 069 (2023) · published 19 October 2023 | Toggle abstract · pdf

  We present the explicit expressions for the matrix product operator (MPO) representation for the local conserved quantities of the Heisenberg chain. The bond dimension of the MPO grows linearly with the locality of the charges. The MPO has more simple form than the local charges themselves, and their Catalan tree patterns naturally emerge from the matrix products. The MPO representation of local conserved quantities is generalized to the integrable SU(N) invariant spin chain.

  4 citations

• Remarks on Berry connection in QFT, anomalies, and applications

  Mykola Dedushenko

  SciPost Phys. 15, 167 (2023) · published 17 October 2023 | Toggle abstract · pdf

  Berry connection has been recently generalized to higher-dimensional QFT, where it can be thought of as a topological term in the effective action for background couplings. Via the inflow, this term corresponds to the boundary anomaly in the space of couplings, another notion recently introduced in the literature. In this note we address the question of whether the old-fashioned Berry connection (for time-dependent couplings) still makes sense in a QFT on $\Sigma^{(d)}× \mathbb{R}$, where $\Sigma^{(d)}$ is a $d$-dimensional compact space and $\mathbb{R}$ is time. Compactness of $\Sigma^{(d)}$ relieves us of the IR divergences, so we only have to address the UV issues. We describe a number of cases when the Berry connection is well defined (which includes the $tt^*$ equations), and when it is not. We also mention a relation to the boundary anomalies and boundary states on the Euclidean $\Sigma^{(d)} × \mathbb{R}_{≥ 0}$. We then work out the examples of a free 3D Dirac fermion and a 3D $\mathcal{N}=2$ chiral multiplet. Finally, we consider 3D theories on $\mathbb{T}^2× \mathbb{R}$, where the space $\mathbb{T}^2$ is a two-torus, and apply our machinery to clarify some aspects of the relation between 3D SUSY vacua and elliptic cohomology. We also comment on the generalization to higher genus.

  6 citations

• Topological holography: Towards a unification of Landau and beyond-Landau physics

  Heidar Moradi, Seyed Faroogh Moosavian, Apoorv Tiwari

  SciPost Phys. Core 6, 066 (2023) · published 16 October 2023 | Toggle abstract · pdf

  We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with a global symmetry in one lower dimension. The global symmetry naturally serves as an input for the topological order. In particular, we holographically construct a String Operator Algebra (SOA) which is the building block of symmetric quantum systems with a given symmetry G in one lower dimension. This exposes a vast web of dualities which act on the space of G-symmetric quantum systems. The SOA facilitates the classification of gapped phases as well as their corresponding order parameters and fundamental excitations, while dualities help to navigate and predict various corners of phase diagrams and analytically compute universality classes of phase transitions. A novelty of the approach is that it treats conventional Landau and unconventional topological phase transitions on an equal footing, thereby providing a holographic unification of these seemingly-disparate domains of understanding. We uncover a new feature of gapped phases and their multi-critical points, which we dub fusion structure, that encodes information about which phases and transitions can be dual to each other. Furthermore, we discover that self-dual systems typically posses emergent non-invertible, i.e., beyond group-like symmetries. We apply these ideas to $1+1d$ quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in $2+1d$. We predict the phase diagrams of various concrete spin models, and analytically compute the full conformal spectra of non-trivial quantum phase transitions, which we then verify numerically.

  47 citations

• From combinatorial maps to correlation functions in loop models

  Linnea Grans-Samuelsson, Jesper Lykke Jacobsen, Rongvoram Nivesvivat, Sylvain Ribault, Hubert Saleur

  SciPost Phys. 15, 147 (2023) · published 9 October 2023 | Toggle abstract · pdf

  In two-dimensional statistical physics, correlation functions of the $O(N)$ and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as ribbon graphs). We allow disconnected maps, but not maps that include monogons. Given a map with $n$ vertices, we obtain a function of the moduli of the corresponding punctured Riemann surface. Due to the map's combinatorial (rather than topological) nature, that function is single-valued, and we call it an $n$-point correlation function. We conjecture that in the critical limit, such functions form a basis of solutions of certain conformal bootstrap equations. They include all correlation functions of the $O(N)$ and Potts models, and correlation functions that do not belong to any known model. We test the conjecture by counting solutions of crossing symmetry for four-point functions on the sphere.

  6 citations

• Flux vacua and modularity for $\mathbb{Z}_2$ symmetric Calabi-Yau manifolds

  Philip Candelas, Xenia de la Ossa, Pyry Kuusela, Joseph McGovern

  SciPost Phys. 15, 146 (2023) · published 9 October 2023 | Toggle abstract · pdf

  We find continuous families of supersymmetric flux vacua in IIB Calabi-Yau compactifications for multiparameter manifolds with an appropriate $\mathbb{Z}_{2}$ symmetry. We argue, supported by extensive computational evidence, that the numerators of the local zeta functions of these compactification manifolds have quadratic factors. These factors are associated with weight-two modular forms, these manifolds being said to be weight-two modular. Our evidence supports the flux modularity conjecture of Kachru, Nally, and Yang. The modular forms are related to a continuous family of elliptic curves. The flux vacua can be lifted to F-theory on elliptically fibred Calabi-Yau fourfolds. If conjectural expressions for Deligne's periods are true, then these imply that the F-theory fibre is complex-isomorphic to the modular curve. In three examples, we compute the local zeta function of the internal geometry using an extension of known methods, which we discuss here and in more detail in a companion paper. With these techniques, we are able to compare the zeta function coefficients to modular form Fourier coefficients for hundreds of manifolds in three distinct families, finding agreement in all cases. Our techniques enable us to study not only parameters valued in $\mathbb{Q}$ but also in algebraic extensions of $\mathbb{Q}$, so exhibiting relations to Hilbert and Bianchi modular forms. We present in appendices the zeta function numerators of these manifolds, together with the corresponding modular forms.

  11 citations

• Mirror symmetry for five-parameter Hulek-Verrill manifolds

  Philip Candelas, Xenia de la Ossa, Pyry Kuusela, Joseph McGovern

  SciPost Phys. 15, 144 (2023) · published 6 October 2023 | Toggle abstract · pdf

  We study the mirrors of five-parameter Calabi-Yau threefolds first studied by Hulek and Verrill in the context of observed modular behaviour of the zeta functions for Calabi-Yau manifolds. Toric geometry allows for a simple explicit construction of these mirrors, which turn out to be familiar manifolds. These are elliptically fibred in multiple ways. By studying the singular fibres, we are able to identify the rational curves of low degree on the mirror manifolds. This verifies the mirror symmetry prediction obtained by studying the mirror map near large complex structure points. We undertake also an extensive study of the periods of the Hulek-Verrill manifolds and their monodromies. On the mirror, we compute the genus-zero and -one instanton numbers, which are labelled by 5 indices, as $h^{1,1}\!=5$. There is an obvious permutation symmetry on these indices, but in addition there is a surprising repetition of values. We trace this back to an $S_{6}$ symmetry made manifest by certain constructions of the complex structure moduli space of the Hulek-Verrill manifold. Among other consequences, we see in this way that the moduli space has six large complex structure limits. It is the freedom to expand the prepotential about any one of these points that leads to this symmetry in the instanton numbers. An intriguing fact is that the group that acts on the instanton numbers is larger than $S_6$ and is in fact an infinite hyperbolic Coxeter group, that we study. The group orbits have a "web" structure, and with certain qualifications the instanton numbers are only nonzero if they belong to what we term "positive webs". This structure has consequences for instanton numbers at all genera.

  7 citations

• Evaluating one-loop string amplitudes

  Lorenz Eberhardt, Sebastian Mizera

  SciPost Phys. 15, 119 (2023) · published 27 September 2023 | Toggle abstract · pdf

  We evaluate one-loop open-string amplitudes at finite $\alpha'$ for the first time. Our method involves a deformation of the integration contour over the modular parameter $\tau$ to a fractal contour introduced by Rademacher in the context of analytic number theory. This procedure leads to explicit and practical formulas for the one-loop four-point amplitudes in type-I superstring theory, amenable to numerical evaluation. We plot the amplitudes as a function of the Mandelstam invariants $s$ and $t$ and directly verify long-standing conjectures about their behaviour at high energies.

  15 citations

• On weak ergodicity breaking in mean-field spin glasses

  Giampaolo Folena, Francesco Zamponi

  SciPost Phys. 15, 109 (2023) · published 21 September 2023 | Toggle abstract · pdf

  The weak ergodicity breaking hypothesis postulates that out-of-equilibrium glassy systems lose memory of their initial state despite being unable to reach an equilibrium stationary state. It is a milestone of glass physics, and has provided a lot of insight on the physical properties of glass aging. Despite its undoubted usefulness as a guiding principle, its general validity remains a subject of debate. Here, we present evidence that this hypothesis does not hold for a class of mean-field spin glass models. While most of the qualitative physical picture of aging remains unaffected, our results suggest that some important technical aspects should be revisited.

  15 citations