arXiv subjects

Kazumi Okuyama

Publications and source records attributed to Kazumi Okuyama.

At least 55 records · Page 3Linked to original sources

arXiv2019

Eigenvalue instantons in the spectral form factor of random matrix model

We study the late time plateau behavior of the spectral form factor in the Gaussian Unitary Ensemble (GUE) random matrix model. The time derivative of the spectral form factor in the plateau regime is not strictly zero, but non-zero due to a non-perturbative correction in the $1/N$ expansion. We argue that such a non-perturbative correction comes from the eigenvalue instanton of random matrix model and we explicitly compute the instanton correction as a function of time.

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arXiv2019

Spectral form factor and semi-circle law in the time direction

We study the time derivative of the connected part of spectral form factor, which we call the slope of ramp, in Gaussian matrix model. We find a closed formula of the slope of ramp at finite $N$ with non-zero inverse temperature. Using this exact result, we confirm numerically that the slope of ramp exhibits a semi-circle law as a function of time.

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arXiv2018

Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM

We study the connected correlator of 1/2 BPS winding Wilson loops in $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory, where those Wilson loops are on top of each other along the same circle. We find the exact finite $N$ expression of the connected correlator of such Wilson loops. We show that the $1/N$ expansion of this exact result is reproduced from the topological recursion of Gaussian matrix model. We also study the exact finite $N$ expression of the generating function of 1/2 BPS Wilson loops in the symmetric representation.

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arXiv2018

Resurgence analysis of 2d Yang-Mills theory on a torus

We study the large $N$ 't Hooft expansion of the partition function of 2d $U(N)$ Yang-Mills theory on a torus. We compute the $1/N$ genus expansion of both the chiral and the full partition function of 2d Yang-Mills using the recursion relation found by Kaneko and Zagier with a slight modification. Then we study the large order behavior of this genus expansion, from which we extract the non-perturbative correction using the resurgence relation. It turns out that the genus expansion is not Borel summable and the coefficient of 1-instanton correction, the so-called Stokes parameter, is pure imaginary. We find that the non-perturbative correction obtained from the resurgence is reproduced from a certain analytic continuation of the grand partition function of a system of non-relativistic fermions on a circle. Our analytic continuation is different from that considered in hep-th/0504221.

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arXiv2018

Phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $θ$-angle

We study the phase diagram of $q$-deformed Yang-Mills theory on $S^2$ at non-zero $θ$-angle using the exact partition function at finite $N$. By evaluating the exact partition function numerically, we find evidence for the existence of a series of phase transitions at non-zero $θ$-angle as conjectured in [hep-th/0509004].

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arXiv2017

Phase Transition of Anti-Symmetric Wilson Loops in $\mathcal{N}=4$ SYM

We will argue that the 1/2 BPS Wilson loops in the anti-symmetric representations in the $\mathcal{N}=4$ super Yang-Mills (SYM) theory exhibit a phase transition at some critical value of the 't Hooft coupling of order $N^2$. In the matrix model computation of Wilson loop expectation values, this phase transition corresponds to the transition between the one-cut phase and the two-cut phase. It turns out that the one-cut phase is smoothly connected to the small 't Hooft coupling regime and the $1/N$ corrections of Wilson loops in this phase can be systematically computed from the topological recursion in the Gaussian matrix model.

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arXiv2017

Wilson loops in unitary matrix models at finite $N$

It is known that the expectation value of Wilson loops in the Gross-Witten-Wadia (GWW) unitary matrix model can be computed exactly at finite $N$ for arbitrary representations. We study the perturbative and non-perturbative corrections of Wilson loops in the $1/N$ expansion, either analytically or numerically using the exact result at finite $N$. As a by-product of the exact result of Wilson loops, we propose a large $N$ master field of GWW model. This master field has an interesting eigenvalue distribution. We also study the Wilson loops in large representations, called Giant Wilson loops, and comment on the Hagedorn/deconfinement transition of a unitary matrix model with a double trace interaction.

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arXiv2016

Wilson loops in 3d $\mathcal{N}=4$ SQCD from Fermi gas

We study 1/2 BPS Wilson loops in 3d $\mathcal{N}=4$ $U(N)$ Yang-Mills theory with one adjoint and $N_f$ fundamental hypermultiplets from the Fermi gas approach. By numerical fitting, we find the first few worldsheet instanton corrections to the Wilson loops with winding numbers 1, 2 and 3. We verify that our Fermi gas results are consistent with the matrix model results in the planar limit.

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arXiv2016

$α'$-expansion of Anti-Symmetric Wilson Loops in $\mathcal{N}=4$ SYM from Fermi Gas

We study the large 't Hooft coupling expansion of 1/2 BPS Wilson loops in the anti-symmetric representation in $ \mathcal{N}=4 $ super Yang-Mills (SYM) theory at the leading order in the 1/N expansion. Via AdS/CFT correspondence, this expansion corresponds to the $α'$ expansion in bulk type IIB string theory. We show that this expansion can be systematically computed by using the low temperature expansion of Fermi distribution function, known as the Sommerfeld expansion in statistical mechanics. We check numerically that our expansion agrees with the exact result of anti-symmetric Wilson loops recently found by Fiol and Torrents.

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arXiv2016

Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory

We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the partition functions.

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arXiv2016

ABJ Theory in the Higher Spin Limit

We study the conjecture made by Chang, Minwalla, Sharma, and Yin on the duality between the N=6 Vasiliev higher spin theory on AdS_4 and the N=6 Chern-Simons-matter theory, so-called ABJ theory, with gauge group U(N) x U(N+M). Building on our earlier results on the ABJ partition function, we develop the systematic 1/M expansion, corresponding to the weak coupling expansion in the higher spin theory, and compare the leading 1/M correction, with our proposed prescription, to the one-loop free energy of the N=6 Vasiliev theory. We find an agreement between the two sides up to an ambiguity that appears in the bulk one-loop calculation.

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arXiv2016

Resummations and Non-Perturbative Corrections

We consider a generalization of the Borel resummation, which turns out to be equivalent to the standard Borel resummation. We apply it to the simplest large N duality between the pure Chern-Simons theory and the topological string on the resolved conifold, and find a simple integral formula for the free energy. Expanding this integral representation around the large radius point at finite string coupling gs, we find that it includes not only the M-theoretic resummation a la Gopakumar and Vafa, but also a non-perturbative correction in gs. Remarkably, the obtained non-perturbative correction is in perfect agreement with a proposal for membrane instanton corrections in arXiv:1306.1734. Various other examples are also presented.

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arXiv2016

Exact results for ABJ Wilson loops and open-closed duality

We find new exact relations between the partition function and vacuum expectation values (VEVs) of 1/2 BPS Wilson loops in ABJ theory, which allow us to predict the large N expansions of the 1/2 BPS Wilson loops from known results of the partition function. These relations are interpreted as an open-closed duality where the closed string background is shifted by the insertion of Wilson loops due to a back-reaction. Using the connection between ABJ theory and the topological string on local P1 x P1, we explicitly write down non-trivial relations between open and closed string amplitudes.

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arXiv2016

Orientifolding of the ABJ Fermi gas

The grand partition functions of ABJ theory can be factorized into even and odd parts under the reflection of fermion coordinate in the Fermi gas approach. In some cases, the even/odd part of ABJ grand partition function is equal to that of $\mathcal{N}=5$ $O(n)\times USp(n')$ theory, hence it is natural to think of the even/odd projection of grand partition function as an orientifolding of ABJ Fermi gas system. By a systematic WKB analysis, we determine the coefficients in the perturbative part of grand potential of such orientifold ABJ theory. We also find the exact form of the first few "half-instanton" corrections coming from the twisted sector of the reflection of fermion coordinate. For the Chern-Simons level $k=2,4,8$ we find closed form expressions of the grand partition functions of orientifold ABJ theory, and for $k=2,4$ we prove the functional relations among the grand partition functions conjectured in arXiv:1410.7658.

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arXiv2016

Numerical Analysis of Coleman-de Luccia Tunneling

We study the false vacuum decay of a single scalar field $ϕ$ coupled to gravity described by the Coleman-de Luccia (CdL) instanton. We show that it is possible to numerically calculate the bounce factor, which is related to the CdL tunneling rate, without using the thin-wall approximation. In this paper, we consider $1/\cosh(ϕ)$- and $\cos(ϕ)$-type potential as examples, which have cosmological and phenomenological applications. Especially, in the $\cos(ϕ)$-type potential we show that the range of values in which axion decay constant can take is restricted by the form of the periodic potential if the CdL tunneling occurs.

hep-ph↗

arXiv2016

TBA-like integral equations from quantized mirror curves

Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in certain cases, this resolvent function satisfies a system of non-linear integral equations whose structure is very similar to the Thermodynamic Bethe Ansatz (TBA) systems. This can be used to compute spectral traces, both exactly and as a semiclassical expansion. As a main example, we consider the system related to the quantized mirror curve of local $\mathbb P^2$. According to a recent proposal, the traces of this operator are determined by the refined BPS indices of the underlying CY. We use our non-linear integral equations to test that proposal.

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arXiv2015

Probing non-perturbative effects in M-theory on orientifolds

Using holography, we study non-perturbative effects in M-theory on orientifolds from the analysis of the S^3 partition functions of dual field theories. We consider the S^3 partition functions of N=4 Yang-Mills theory with O(n) gauge symmetry coupled to one (anti)symmetric and N_f fundamental hypermultiplets from the Fermi gas approach. In addition to the worldsheet instanton and membrane instanton corrections to the grand potential, which are also present in the U(n) Yang-Mills case, we find that there exist "half instanton" corrections coming from the effect of orientifold plane.

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arXiv2015

Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories

We investigate the large $N$ instanton effects of partition functions in a class of $\mathcal{N}=4$ circular quiver Chern-Simons theories on a three-sphere. Our analysis is based on the supersymmetry localization and the Fermi-gas formalism. The resulting matrix model can be regarded as a two-parameter deformation of the ABJM matrix model, and has richer non-perturbative structures. Based on a systematic semi-classical analysis, we find analytic expressions of membrane instanton corrections. We also exactly compute the partition function for various cases and find some exact forms of worldsheet instanton corrections, which appear as quantum mechanical non-perturbative corrections in the Fermi-gas system.

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