arXiv subjects

Min-xin Huang

Publications and source records attributed to Min-xin Huang.

At least 19 recordsLinked to original sources

arXiv2026

Superconformal index for $\mathcal{N} = 4$ Super Yang-Mills and Elliptic Macdonald Polynomials

We establish a connection between the superconformal index of $\mathcal{N}=4$ $U(N)$ SYM and the elliptic Ruijsenaars-Schneider integrable system. The index admits an expression in terms of elliptic Macdonald polynomials, which leads to a compact summation over generalized partitions involving the structure constants $B_λ(p,q,t)$ and normalization constants $\mathcal{N}_λ(p,q,t)$. By solving the elliptic Ruijsenaars-Schneider model perturbatively in the elliptic parameter $p$, a systematic expansion of the index in powers of $p$ is obtained. We check that in various limits, namely a deformed 1/2 BPS limit and especially the large $N$ limit, our formalism reduces to previously known results.

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arXiv2026

Gibbons-Hawking Entropy and BMN Strings

We provide some up-to-date discussions related to cosmological event horizon and entropy of our universe, then introduce an intriguing idea that there may be a universal finite upper bound for entropy accessible to an observer in consistent theories of quantum gravity. We argue that the Berenstein-Maldacena-Nastase (BMN) strings provide a test of the idea. More speculatively, in an optimistic scenario, this also provides a possible estimate of the cosmological constant.

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arXiv2026

Deformed Schur Indices of BCD-type for N=4 Super Yang-Mills and Symmetric Functions

We investigate the deformed Schur index in four dimensional N=4 super Yang-Mills theories with $SO$ and $Sp$ gauge groups, generalizing Hatsuda's recent calculations. We express the deformed Schur index as integrals of Koornwinder polynomials and Macdonald polynomials, then perform the integrals in terms of the normalization constants of Macdonald polynomials. We provide explicit results for some low rank gauge groups and for expansion in a $u$ parameter. We discuss various special limits and the tests of S-duality.

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arXiv2025

Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops

We relate the counting of refined BPS numbers on compact elliptically fibred Calabi-Yau threefolds $X$ to Wilson loop expectations values in the gauge theories that emerge in various rigid local limits of the 5d supergravity theory defined by M-theory compactification on $X$. In these local limits $X_*$ the volumes of curves in certain classes go to infinity, the corresponding very massive M2-brane states can be treated as Wilson loop particles and the refined topological string partition function on $X$ becomes a sum of terms proportional to associated refined Wilson loop expectation values. The resulting ansatz for the complete refined topological partition function on $X$ is written in terms of the proportionality coefficients which depend only on the $ε$ deformations and the Wilson loop expectations values which satisfy holomorphic anomaly equations. Since the ansatz is quite restrictive and can be further constrained by the one-form symmetries and E-string type limits for large base curves, we can efficiently evaluate the refined BPS numbers on $X$, which we do explicitly for local gauge groups up to rank three and $h_{11}(X)=5$. These refined BPS numbers pass an impressive number of consistency checks imposed by the direct counting of these numbers using the moduli space of one dimensional stable sheaves on $X$ and give us numerical predictions for the complex structure dependency of the refined BPS numbers.

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arXiv2023

Schur indices for $\mathcal{N}=4$ super-Yang-Mills with more general gauge groups

We study the unflavored Schur indices in the $\mathcal{N}=4$ super-Yang-Mills theory for the $B_n,C_n,D_n, G_2$ gauge groups. We explore two methods, namely the character expansion method and the Fermi gas method, to efficiently compute the $q$-series expansion of the Schur indices to some high orders. Using the available data and the modular properties, we are able to fix the exact formulas for the general gauge groups up to some high ranks and discover some interesting new features. We also identify some empirical modular anomaly equations, but unlike the case of $A_n$ groups, they are quite complicated and not sufficiently useful to fix exact formulas for gauge groups of arbitrary rank.

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arXiv2023

Thermal Entropy in Calabi-Yau Quantum Mechanics

We consider the von Neumann entropy of a thermal mixed state in quantum systems derived from mirror curves, where the kinetic terms are exponential functions of the momentum operators. Using the mathematical results on the asymptotics of the energy eigenvalues, we compute the asymptotic entropy in high temperature limit and compare with that of the conventional models. We discuss the connections with some folklores in quantum gravity, particularly on the finiteness of entropy.

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arXiv2023

Krylov Complexity in Calabi-Yau Quantum Mechanics

Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries, as well as some non-relativistic models. We find that for the Calabi-Yau models, the Lanczos coefficients grow slower than linearly for small $n$'s, consistent with the behavior of integrable models. On the other hand, for the non-relativistic models, the Lanczos coefficients initially grow linearly for small $n$'s, then reach a plateau. Although this looks like the behavior of a chaotic system, it is mostly likely due to saddle-dominated scrambling effects instead, as argued in the literature. In our cases, the slopes of linearly growing Lanczos coefficients almost saturate a bound by the temperature. During our study, we also provide an alternative general derivation of the bound for the slope.

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arXiv2022

Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills

We propose a novel modular anomaly equation for the unflavored Schur index in the $\mathcal{N}=4$ $SU(N)$ super-Yang-Mills theory. The vanishing conditions overdetermine the modular ambiguity ansatz from the equation, thus together they are sufficient to recursively compute the exact Schur indices for all $SU(N)$ gauge groups. Using the representations as MacMahon's generalized sum-of-divisors functions and Jacobi forms, we then prove our proposal as well as elucidate a general formula conjectured by Pan and Peelaers.

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arXiv2022

Topological strings and Wilson loops

We propose the refined topological string correspondence to the expectation values of half-BPS Wilson loop operators in 5d $\mathcal{N}=1$ gauge theory partition function on the Omega-deformed background $\mathbb{R}^4_{ε_{1,2}}\times S^1$. We provide the refined topological vertex method and the refined holomorphic anomaly equation method in the topological string theory, from which we have exact computations on the 5d Wilson loops partition functions in both A- and B-models. Finally, with the exact results we have in B-model, we recover the quantum periods of local $\mathbb{P}^1\times\mathbb{P}^1$ model and local $\mathbb{P}^2$ model in the study of quantum geometry and we further give a refined generalization of A-period.

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arXiv2021

Bootstrapping Calabi-Yau Quantum Mechanics

Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau geometries, where the exact quantization conditions have been conjecturally related to topological string theory. We find that the bootstrap method provides a promising alternative for the precision numerical calculations of the energy eigenvalues. An improvement in our approach is to use a larger set of two-dimensional operators instead of one-dimensional ones. We also apply our improved bootstrap methods to some non-relativistic models in the recent literature and demonstrate better numerical accuracies.

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arXiv2021

Non-Negativity of BMN Two-Point Functions With Three String Modes

Recently, we proposed a novel entry of the pp-wave holographic dictionary, which equated the Berenstein-Maldacena-Nastase (BMN) two-point functions in free $\mathcal{N}=4$ super-Yang-Mills theory with the norm squares of the quantum unitary transition amplitudes between the corresponding tensionless strings in the infinite curvature limit, for the cases with no more than three string modes in different transverse directions. A seemingly highly non-trivial conjectural consequence, particularly in the case of three string modes, is the non-negativity of the BMN two-point functions at any higher genus for any mode numbers. In this paper, we further perform the detailed calculations of the BMN two-point functions with three string modes at genus two, and explicitly verify that they are always non-negative through mostly extensive numerical tests.

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arXiv2021

Boson-Fermion Correspondence and Holomorphic Anomaly Equation in 2d Yang-Mills Theory on Torus

Recently, Okuyama and Sakai proposed a novel holomorphic anomaly equation for the partition function of 2d Yang-Mills theory on a torus, based on an anholomorphic deformation of the propagator in the bosonic formulation. Using the boson-fermion correspondence, we derive the formula for the deformed partition function in fermionic description and give a proof of the holomorphic anomaly equation.

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arXiv2021

Free BMN Correlators With More Stringy Modes

In the type IIB maximally supersymmetric pp-wave background, stringy excited modes are described by BMN (Berenstein-Madalcena-Nastase) operators in the dual $\mathcal{N}=4$ super-Yang-Mills theory. In this paper, we continue the studies of higher genus free BMN correlators with more stringy modes, mostly focusing on the case of genus one and four stringy modes in different transverse directions. Surprisingly, we find that the non negativity of torus two-point functions, which is a consequence of a previously proposed probability interpretation and has been verified in the cases with two and three stringy modes, is no longer true for the case of four or more stringy modes. Nevertheless, the factorization formula, which is also a proposed holographic dictionary relating the torus two-point function to a string diagram calculation, is still valid. We also check the correspondence of planar three-point functions with Green-Schwarz string vertex with many string modes. We discuss some issues in the case of multiple stringy modes in the same transverse direction. Our calculations provide some new perspectives on pp-wave holography.

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arXiv2021

Note on Quantum Periods and a TBA-like System

There is an interesting relation between the quantum periods on a certain limit of local $\mathbb{P}^1\times \mathbb{P}^1$ Calabi-Yau space and a TBA (Thermodynamic Bethe Ansatz) system appeared in the studies of ABJM (Aharony-Bergman-Jafferis-Maldacena) theory. We propose a one-parameter generalization of the relation. Furthermore, we derive the differential operators for quantum periods and the TBA-like equation in various limits of the generalized relation.

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arXiv2020

Quantum Periods and TBA-like Equations for a Class of Calabi-Yau Geometries

We continue the study of a novel relation between quantum periods and TBA(Thermodynamic Bethe Ansatz)-like difference equations, generalize previous works to a large class of Calabi-Yau geometries described by three-term quantum operators. We give two methods to derive the TBA-like equations. One method uses only elementary functions while the other method uses Faddeev's quantum dilogarithm function. The two approaches provide different realizations of TBA-like equations which are nevertheless related to the same quantum period.

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arXiv2020

Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries

We study a class of quantum integrable systems derived from dimer graphs and also described by local toric Calabi-Yau geometries with higher genus mirror curves, generalizing some previous works on genus one mirror curves. We compute the spectra of the quantum systems both by standard perturbation method and by Bohr-Sommerfeld method with quantum periods as the phase volumes. In this way, we obtain some exact analytic results for the classical and quantum periods of the Calabi-Yau geometries. We also determine the differential operators of the quantum periods and compute the topological string free energy in Nekrasov-Shatashvili (NS) limit. The results agree with calculations from other methods such as the topological vertex.

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arXiv2020

Towards Refining the Topological Strings on Compact Calabi-Yau 3-folds

We make a proposal for calculating refined Gopakumar-Vafa numbers (GVN) on elliptically fibered Calabi-Yau 3-folds based on refined holomorphic anomaly equations. The key examples are smooth elliptic fibrations over (almost) Fano surfaces. We include a detailed review of existing mathematical methods towards defining and calculating the (unrefined) Gopakumar-Vafa invariants (GVI) and the GVNs on compact Calabi-Yau 3-folds using moduli of stable sheaves, in a language that should be accessible to physicists. In particular, we discuss the dependence of the GVNs on the complex structure moduli and on the choice of an orientation. We calculate the GVNs in many instances and compare the B-model predictions with the geometric calculations. We also derive the modular anomaly equations from the holomorphic anomaly equations by analyzing the quasi-modular properties of the propagators. We speculate about the physical relevance of the mathematical choices that can be made for the orientation.

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arXiv2020

Note on S-channel factorization in multitrace Berenstein-Maldacena-Nastase correlators

In a previous paper we proposed a factorization principle for the correlation functions of Berenstein-Maldacena-Nastase (BMN) operators in free $\mathcal{N}=4$ super-Yang-Mills theory. These correlators are conjectured to described physical string amplitudes in an infinitely curved Ramond-Ramond pp-wave background. There was a puzzle that the factorization seems to break down for $S$-channel in the $2\rightarrow 2$ scattering process. Here we resolve this puzzle by including some diagrams missed in the previous paper. We also observe some interesting relations which further support the interpretation of higher genus correlators as physical string loop amplitudes.

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