Searcharxiv⌕ Search

arXiv subjects

Joseph A. Minahan

Publications and source records attributed to Joseph A. Minahan.

At least 19 recordsLinked to original sources
arXiv2026

The growth of $SO(9)$ super-representations in Type II string theory

We study the growth of massive $SO(9)$ super-representations in type II and type I string theories. We do this first directly by finding an empirical formula that specifies which representations appear at any level, and then compute the multiplicities from a refined partition function evaluated over finite fields up to level 501 for individual representations, and level 226 for all representations. We then derive asymptotic formulae for the growth of any representation, which are constructed by integrating about the peaks of the refined partition function. Using a Rademacher sum we can find very accurate approximations for the multiplicities of the representations. Unlike the superstring partition function, which only receives contributions from the odd Rademacher terms, the multiplicities for any representation have contributions from both even and odd terms. Finally, we apply the same techniques to the ordinary representations, where a simplified refined partition function allows for better computational speed and simpler expressions for the asymptotic approximations.

hep-th↗
arXiv2026

Two-point functions in $4-2\,\varepsilon$ dimensions from localization

We study two-point functions of half-BPS operators in maximally supersymmetric Yang-Mills theory continued to $d=4-2\,\varepsilon$ dimensions. Using supersymmetric localization on $S^d$, we derive perturbative matrix-model expressions for the $\varepsilon$-expansion of these correlators and obtain all-loop results at leading order in $\varepsilon$ in the planar limit, with extensions to finite-$N$ corrections and higher-charge operators. We compare the localization results with direct perturbative computations in flat space. At order $\varepsilon$ the two descriptions agree perfectly, while at higher orders our construction fails to reproduce the perturbative data due to the breaking of conformal symmetry away from four dimensions. Nevertheless, in the case of the dimension-two operator we conjecture an all-loop formula at order $\varepsilon^2$ by exploiting the precise form of the mismatch.

hep-th↗
arXiv2025

Twisting the Hagedorn temperature in planar $\mathcal{N}=4$ super Yang-Mills

We consider planar $\mathcal{N}=4$ super Yang-Mills at finite temperature with chemical potentials that couple either to the $R$-charges or the spins of the operators. We find expressions for the Hagedorn temperatures at both zero coupling by explicitly counting states, and at strong coupling using the string theory dual. We then apply the quantum spectral curve (QSC) to this problem, which adds additional twists to the $Q$-functions. For a single chemical potential $μ$ coupled to one of the $R$-charges, we find the analytic weak-coupling Hagedorn temperature to one-loop order for any value of $μ$, and to two-loop order for $μ=1/2$. We then solve the QSC numerically, showing that at strong coupling there is good agreement with the string theory prediction to order $1/λ^{1/4}$. This provides further evidence for a recent conjecture of Harmark for the form of the world-sheet zero-point shift. We also use the QSC to find the analytic one-loop correction to the Hagedorn temperature with non-zero chemical potentials coupled to the spins.

hep-th↗
arXiv2023

The ABJM Hagedorn Temperature from Integrability

We use the quantum spectral curve to compute the Hagedorn temperature for ABJM theory in terms of the interpolating function $h(λ)$. At weak coupling we compute this temperature up to eight-loop order, showing that it matches the known tree-level and two-loop results. At strong coupling we compute the dependence numerically, showing that it is consistent with expectations from supergravity and the plane-wave limit for the four leading terms in the strong coupling expansion, up to an overall shift of the zero-point energy for type IIA string theory on AdS$_4\times \mathbb{C}\textrm{P}^3$. We conjecture an analytic form for this shift to leading order that is consistent with our numerical results.

hep-th↗
arXiv2023

The asymptotic form of the Hagedorn temperature in planar $\mathcal{N}=4$ super Yang-Mills

Using the supergravity dual and the plane-wave limit as a guide, we conjecture the asymptotic large coupling form of the Hagedorn temperature for planar $\mathcal{N}=4$ super Yang-Mills to order $1/\sqrtλ$. This is two orders beyond the presently known behavior. Using the quantum spectral curve procedure of Harmark and Wilhelm, we show that our conjectured form is in excellent agreement with the numerical results.

hep-th↗
arXiv2022

Seven-dimensional super Yang-Mills at negative coupling

We consider the partition function for Euclidean $SU(N)$ super Yang-Mills on a squashed seven-sphere. We show that the localization locus of the partition function has instanton membrane solutions wrapping the six "fixed" three-spheres on the $\mathbb{S}^7$. The ADHM variables of these instantons are fields living on the membrane world volume. We compute their contribution by localizing the resulting three-dimensional supersymmetric field theory. In the round-sphere limit the individual instanton contributions are singular, but the singularities cancel when adding the contributions of all six three-spheres. The full partition function on the ${\mathbb S}^7$ is well-defined even when the square of the effective Yang-Mills coupling is negative. We show for an $SU(2)$ gauge theory in this regime that the bare negative tension of the instanton membranes is canceled off by contributions from the instanton partition function, indicating the existence of tensionless membranes. We provide evidence that this phase is distinct from the usual weakly coupled super Yang-Mills and, in fact, is gravitational.

hep-th↗
arXiv2021

Conformal field theories on deformed spheres, anomalies, and supersymmetry

We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then specialize to $\mathcal{N}=2$ SCFTs where one can preserve some supersymmetry on a compact manifold by turning on appropriate background fields. For deformations of the round sphere the $c$ anomaly receives corrections proportional to the supersymmetric completion of the (Weyl)$^2$ term, which we determine up to one constant by analyzing the scale dependence of various correlators in the stress-tensor multiplet. We further show that the double derivative of the free energy with respect to the marginal couplings is proportional to the two-point function of the bottom components of the marginal chiral multiplet placed at the two poles of the deformed sphere. We then use anomaly considerations and counter-terms to parametrize the finite part of the free energy which makes manifest its dependence on the Kähler potential. We demonstrate these results for a theory with a vector multiplet and a massless adjoint hypermultiplet using results from localization. Finally, by choosing a special value of the hypermultiplet mass where the free energy is independent of the deformation, we derive an infinite number of constraints between various integrated correlators in $\mathcal{N}=4$ super Yang-Mills with any gauge group and at all values of the coupling, extending previous results.

hep-th↗
arXiv2020

Five-dimensional gauge theories on spheres with negative couplings

We consider supersymmetric gauge theories on $S^5$ with a negative Yang-Mills coupling in their large $N$ limits. Using localization we compute the partition functions and show that the pure ${\mathrm{SU}}(N)$ gauge theory descends to an ${\mathrm{SU}}(N/2)_{+N/2}\times {\mathrm{SU}}(N/2)_{-N/2}\times {\mathrm{SU}}(2)$ Chern-Simons gauge theory as the inverse 't Hooft coupling is taken to negative infinity for $N$ even. The Yang-Mills coupling of the ${\mathrm{SU}}(N/2)_{\pm N/2}$ is positive and infinite, while that on the ${\mathrm{SU}}(2)$ goes to zero. We also show that the odd $N$ case has somewhat different behavior. We then study the ${\mathrm{SU}}(N/2)_{N/2}$ pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals $1$ in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider ${\mathrm{USp}}(2N)$ theories with an antisymmetric hypermultiplet and $N_f<8$ fundamental hypermultiplets and carry out a similar analysis. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the ${\mathrm{SU}}(N)$ theories in the large $N$ limit.

hep-th↗
arXiv2019

Notes on anomalies, elliptic curves and the BS-D conjecture

We consider anomaly cancellation for $SU(N)\times SU(2)\times U(1)$ gauge theories where the left-handed chiral multiplets are in higher $SU(2)$ representations. In particular, if the left-handed quarks and leptons transform under the triplet representation of $SU(2)$ and if the $U(1)$ gauge group is compact then up to an overall scaling there is only one possible nontrivial assignment for the hypercharges if $N=3$, and two if $N=9$. Otherwise there are infinitely many. We use the Mordell-Weil theorem, Mazur's theorem and the Cremona elliptic curve database which uses Kolyvagin's theorem on the Birch Swinnerton-Dyer conjecture to prove these statements.

hep-th↗
arXiv2019

Supersymmetric Yang-Mills, Spherical Branes, and Precision Holography

Using supersymmetric localization we compute the free energy and BPS Wilson loop vacuum expectation values for planar maximally supersymmetric Yang-Mills theory on $S^d$ in the strong coupling limit for $2\leq d<6$. The same calculation can also be performed in supergravity using the recently found spherical brane solutions. We find excellent agreement between the two sets of results. This constitutes a non-trivial precision test of holography in a non-conformal setting. The free energy of maximal SYM on $S^6$ diverges in the strong coupling limit which might signify the onset of little string theory. We show how this divergence can be regularized both in QFT and in supergravity. We also consider $d=7$ with a small negative 't Hooft coupling and show that the free energy and Wilson loop vacuum expectation value agree with the results from supergravity after addressing some subtleties.

hep-th↗
arXiv2018

Gauge theories on spheres with 16 supercharges and non-constant couplings

We construct a class of theories with 16 supersymmetries on spheres of dimension nine and less. The gauge coupling and mass terms for the scalar fields depend on the polar angle away from the north pole. Assuming finite coupling on the north pole, this leads to zero coupling at the south pole for $d>4$ and infinite coupling at the south pole for $d<4$. The underlying supersymmetry algebra of these theories is shown to be isomorphic to the Poincaré superalgebra in $d$-dimensions. We also give a localization procedure which leads to nontrivial results for $d=2$.

hep-th↗
arXiv2018

Analytic continuation of dimensions in supersymmetric localization

We compute the perturbative partition functions for gauge theories with eight supersymmetries on spheres of dimension $d\le5$, proving a conjecture by the second author. We apply similar methods to gauge theories with four supersymmetries on spheres with $d\le3$. The results are valid for non-integer $d$ as well. We further propose an analytic continuation from $d=3$ to $d=4$ that gives the perturbative partition function for an $\mathcal{N}=1$ gauge theory. The results are consistent with the free multiplets and the one-loop $β$-functions for general $\mathcal{N}=1$ gauge theories. We also consider the analytic continuation of an $\mathcal{N}=1$-preserving mass deformation of the maximally supersymmetric gauge theory and compare to recent holographic results for $\mathcal{N}=1^*$ super Yang-Mills. We find that the general structure for the real part of the free energy coming from the analytic continuation is consistent with the holographic results.

hep-th↗
arXiv2017

One-loop tests of supersymmetric gauge theories on spheres

We show that a recently conjectured form for perturbative supersymmetric partition functions on spheres of general dimension $d$ is consistent with the flat space limit of 6-dimensional $\mathcal{N}=1$ super Yang-Mills. We also show that the partition functions for $\mathcal{N}=1$ 8- and 9-dimensional theories are consistent with their known flat space limits.

hep-th↗
arXiv2016

Matrix models for 5d super Yang-Mills

In this contribution to the review on localization in gauge theories we investigate the matrix models derived from localizing N=1 super Yang-Mills on S^5. We consider the large-N limit and attempt to solve the matrix model by a saddle-point approximation. In general it is not possible to find an analytic solution, but at the weak and the strong limits of the 't Hooft coupling there are dramatic simplifications that allows us to extract most of the interesting information. At weak coupling we show that the matrix model is close to the Gaussian matrix model and that the free-energy scales as N^2. At strong coupling we show that if the theory contains one adjoint hypermultiplet then the free-energy scales as N^3. We also find the expectation value of a supersymmetric Wilson loop that wraps the equator. We demonstrate how to extract the effective couplings and reproduce results of Seiberg. Finally, we compare to results for the six-dimensional (2,0) theory derived using the AdS/CFT correspondence. We show that by choosing the hypermultiplet mass such that the supersymmetry is enhanced to N=2, the Wilson loop result matches the analogous calculation using AdS/CFT. The free-energies differ by a rational fraction.

hep-th↗
arXiv2016

Gauge theories with 16 supersymmetries on spheres

We give a unified approach to localization of maximally symmetric gauge theories on spheres, including $S^6$ and $S^7$. The approach follows Pestun's method of dimensionally reducing from 10 dimensional super Yang-Mills. The resulting theories have a reduced $R$-symmetry which includes an $SU(1,1)$ subgroup, except in four dimensions where, because of conformal invariance, the full flat-space $R$-symmetry is maintained, and in seven dimensions where $SU(1,1)$ is the flat-space $R$-symmetry. For the case of $S^6$ and $S^7$ we discuss the localization of these theories and also present new results for the corresponding matrix models. The matrix models for $S^6$ and $S^7$ are qualitatively similar to the matrix models of a vector multiplet on $S^4$ and $S^5$ respectively. We also discuss the contributions of instantons in the six and seven dimensional cases.

hep-th↗
arXiv2016

Localizing gauge theories on $S^d$

We conjecture the form of the one-loop determinants for localized gauge theories with eight supersymmetries on $d$-dimensional spheres. Combining this with results for the localized action, we investigate the strong coupling behavior in the large $N$ limit for a continuous range of $d$. In particular, we find the $N$ dependence of the free energy for supersymmetric Yang-Mills with only a vector multiplet in $3<d<4$ and for maximally supersymmetric Yang-Mills in $3< d<6$. We also argue that this gives an effective way to regularize divergences after localization in $d=4$ for ${\mathcal N}=2$ gauge theories and $d=6$ for the maximally supersymmetric case.

hep-th↗
arXiv2016

Three-point correlators from string amplitudes: Mixing and Regge spins

This paper has two parts. We first compute the leading contribution to the strong-coupling mixing between the Konishi operator and a double-trace operator composed of chiral primaries by using flat-space vertex operators for the string-duals of the operators. We then compute the three-point functions for protected or unprotected scalar operators with higher spin operators on the leading Regge trajectory. Here we see that the nontrivial spatial structures required by conformal invariance arise naturally from the form of the polarization tensors in the vertex operators. We find agreement with recent results extracted from Mellin amplitudes for four-point functions, as well as with earlier supergravity calculations. We also obtain some new results for other combinations of operators.

hep-th↗