arXiv subjects

Masazumi Honda

Publications and source records attributed to Masazumi Honda.

At least 55 records · Page 3Linked to original sources

arXiv2017

Resumming perturbative series in the presence of monopole bubbling effects

Monopole bubbling effect is screening of magnetic charges of singular Dirac monopoles by regular 't Hooft-Polyakov monopoles. We study properties of weak coupling perturbative series in the presence of monopole bubbling effects as well as instantons. For this purpose, we analyze supersymmetric 't Hooft loop in four dimensional $\mathcal{N}=2$ supersymmetric gauge theories with Lagrangians and non-positive beta functions. We show that the perturbative series of the 't Hooft loop is Borel summable along positive real axis for fixed instanton numbers and screened magnetic charges. It turns out that the exact result of the 't Hooft loop is the same as the sum of the Borel resummations over instanton numbers and effective magnetic charges. We also obtain the same result for supersymmetric dyonic loops.

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arXiv2017

ABJ Quadrality

We study physical consequences of adding orientifolds to the ABJ triality, which is among 3d N=6 superconformal Chern-Simons theory known as ABJ theory, type IIA string in AdS_4 x CP^3 and N=6 supersymmetric (SUSY) Vasiliev higher spin theory in AdS_4. After adding the orientifolds, it is known that the gauge group of the ABJ theory becomes O(N_1)xUSp(2N_2) while the background of the string theory is replaced by AdS_4 x CP^3/Z_2, and the supersymmetries in the both theories reduce to N=5. We propose that adding the orientifolds to the N=6 Vasiliev theory leads to N=5 SUSY Vasiliev theory. It turns out that the N=5 case is more involved because there are two formulations of the N=5 Vasiliev theory with either O or USp internal symmetry. We show that the two N=5 Vasiliev theories can be understood as certain projections of the N=6 Vasiliev theory, which we identify with the orientifold projections in the Vasiliev theory. We conjecture that the O(N_1)xUSp(2N_2) ABJ theory has the two vector model like limits: N_2 >> N_1 and N_1 >> N_2 which correspond to the semi-classical N=5 Vasiliev theories with O(N_1) and USp(2N_2) internal symmetries respectively. These correspondences together with the standard AdS/CFT correspondence comprise the ABJ quadrality among the N=5 ABJ theory, string/M-theory and two N=5 Vasliev theories. We provide a precise holographic dictionary for the correspondences by comparing correlation functions of stress tensor and flavor currents. Our conjecture is supported by various evidence such as agreements of the spectra, one-loop free energies and SUSY enhancement on the both sides. We also predict the leading free energy of the N=5 Vasiliev theory from the CFT side. As a byproduct, we give a derivation of the relation between the parity violating phase in the N=6 Vasiliev theory and the parameters in the N=6 ABJ theory, which was conjectured in arXiv:1207.4485.

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arXiv2017

O($N$) Invariance of the Multi-Field Bounce

In his 1977 paper on vacuum decay in field theory: The Fate of the False Vacuum, Coleman considered the problem of a single scalar field and assumed that the minimum action tunnelling field configuration, the bounce, is invariant under O(4) rotations in Euclidean space. A proof of the O(4) invariance of the bounce was provided later by Coleman, Glaser, and Martin (CGM), who extended the proof to $N>2$ Euclidean dimensions but, again, restricted non-trivially to a single scalar field. As far as we know a proof of O($N$) invariance of the bounce for the tunnelling problem with multiple scalar fields has not been reported, even though it was assumed in many works since, being of phenomenological interest. We make progress towards closing this gap. Following CGM we define the reduced problem of finding a field configuration minimizing the kinetic energy at fixed potential energy. Given a solution of the reduced problem, the minimum action bounce can always be obtained from it by means of a scale transformation. We show that if a solution of the reduced problem exists, then it and the minimum action bounce derived from it are indeed O($N$) symmetric.

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arXiv2017

S-duality invariant perturbation theory improved by holography

We study anomalous dimensions of unprotected low twist operators in the four-dimensional $SU(N)$ $\mathcal{N}=4$ supersymmetric Yang-Mills theory. We construct a class of interpolating functions to approximate the dimensions of the leading twist operators for arbitrary gauge coupling $τ$. The interpolating functions are consistent with previous results on the perturbation theory, holographic computation and full S-duality. We use our interpolating functions to test a recent conjecture by the $\mathcal{N}=4$ superconformal bootstrap that upper bounds on the dimensions are saturated at one of the duality-invariant points $τ=i$ and $τ=e^{iπ/3}$. It turns out that our interpolating functions have maximum at $τ=e^{iπ/3}$, which are close to the conjectural values by the conformal bootstrap. In terms of the interpolating functions, we draw the image of conformal manifold in the space of the dimensions. We find that the image is almost a line despite the conformal manifold is two-dimensional. We also construct interpolating functions for the subleading twist operator and study level crossing phenomenon between the leading and subleading twist operators. Finally we study the dimension of the Konishi operator in the planar limit. We find that our interpolating functions match with numerical result obtained by Thermodynamic Bethe Ansatz very well. It turns out that analytic properties of the interpolating functions reflect an expectation on a radius of convergence of the perturbation theory.

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arXiv2017

Cardy Formula for 4d SUSY Theories and Localization

We study 4d $\mathcal{N}=1$ supersymmetric theories on a compact Euclidean manifold of the form $S^1 \times\mathcal{M}_3$. Partition functions of gauge theories on this background can be computed using localization, and explicit formulas have been derived for different choices of the compact manifold $\mathcal{M}_3$. Taking the limit of shrinking $S^1$, we present a general formula for the limit of the localization integrand, derived by simple effective theory considerations, generalizing the result of arXiv:1512.03376. The limit is given in terms of an effective potential for the holonomies around the $S^1$, whose minima determine the asymptotic behavior of the partition function. If the potential is minimized in the origin, where it vanishes, the partition function has a Cardy-like behavior fixed by $\mathrm{Tr}(R)$, while a nontrivial minimum gives a shift in the coefficient. In all the examples that we consider, the origin is a minimum if $\mathrm{Tr}(R) \leq 0$.

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arXiv2016

Exact Path Integral for 3D Higher Spin Gravity

Extending the works arXiv:1504.05991 and arXiv:1510.02142, we study three dimensional Euclidean higher spin gravity with negative cosmological constant. This theory can be formulated in terms of SL(N,C) Chern-Simons theory. By introducing auxiliary fields, we rewrite it in a supersymmetric way and compute its partition function exactly by using the localization method. We obtain a good expression for the partition function in terms of characters for the vacuum and primaries in 2D unitary CFT with W_N symmetry. We also check that the coefficients of the character expansion are positive integers and exhibit Cardy formula in the large central charge limit.

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arXiv2016

How to resum perturbative series in 3d N=2 Chern-Simons matter theories

Continuing the work arXiv:1603.06207, we study perturbative series in general 3d $\mathcal{N}=2$ supersymmetric Chern-Simons matter theory with $U(1)_R$ symmetry, which is given by a power series expansion of inverse Chern-Simons levels. We find that the perturbative series are usually non-Borel summable along positive real axis for various observables. Alternatively we prove that the perturbative series are always Borel summable along negative (positive) imaginary axis for positive (negative) Chern-Simons levels. It turns out that the Borel resummations along this direction are the same as exact results and therefore correct ways of resumming the perturbative series.

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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

Exact relations between M2-brane theories with and without Orientifolds

We study partition functions of low-energy effective theories of M2-branes, whose type IIB brane constructions include orientifolds. We mainly focus on circular quiver superconformal Chern-Simons theory on $S^3$, whose gauge group is $O(2N+1)\times USp(2N)\times \cdots \times O(2N+1)\times USp(2N)$. This theory is the natural generalization of the $\mathcal{N}=5$ ABJM theory with the gauge group $O(2N+1)_{2k} \times USp(2N)_{-k}$. We find that the partition function of this type of theory has a simple relation to the one of the M2-brane theory without the orientifolds, whose gauge group is $U(N)\times \cdots \times U(N)$. By using this relation, we determine an exact form of the grand partition function of the $O(2N+1)_{2} \times USp(2N)_{-1}$ ABJM theory, where its supersymmetry is expected to be enhanced to $\mathcal{N}=6$. As another interesting application, we discuss that our result gives a natural physical interpretation of a relation between the grand partition functions of the $U(N+1)_4 \times U(N)_{-4}$ ABJ theory and $U(N)_2 \times U(N)_{-2}$ ABJM theory, recently conjectured by Grassi-Hatsuda-Mariño. We also argue that partition functions of $\hat{A}_3$ quiver theories have representations in terms of an ideal Fermi gas systems associated with $\hat{D}$-type quiver theories and this leads an interesting relation between certain $U(N)$ and $USp(2N)$ supersymmetric gauge theories.

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arXiv2016

Borel summability of perturbative series in 4d N=2 and 5d N=1 theories

We study weak coupling perturbative series in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in zero instanton sector are Borel summable for various observables. Our result for 4d $\mathcal{N}=2$ case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely Borel summable. We also prove that the perturbative series in arbitrary number of instanton sector are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations in each number of instanton sector.

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arXiv2016

N=2 minimal model from 4d supersymmetric theory

Previous studies have shown that supersymmetric partition function on $T^2 \times S^2$ is related to elliptic genus of two dimensional supersymmetric theory. In this short note we find a four dimensional supersymmetric theory, whose partition function on $T^2 \times S^2$ is the same as elliptic genera of $\mathcal{N}=2$ minimal models in two dimensions.

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arXiv2015

Exact Path Integral for 3D Quantum Gravity II

Continuing the work arXiv:1504.05991, we discuss various aspects of three dimensional quantum gravity partition function in AdS in the semi-classical limit. The partition function is holomorphic and is the one which we obtained by using the localization technique of Chern-Simons theory in arXiv:1504.05991. We obtain a good expression for it in the summation form over Virasoro characters for the vacuum and primaries. A key ingredient for that is an interpretation of boundary localized fermion. We also check that the coefficients in the summation form over Virasoro characters of the partition function are positive integers and satisfy the Cardy formula. These give physical interpretation that these coefficients represent the number of primary fields in the dual CFT in the large k limit.

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arXiv2015

Identification of Bulk coupling constant in Higher Spin/ABJ correspondence

We study the conjectured duality between the $\mathcal{N}=6$ Vasiliev higher spin theory on $AdS_4$ and 3d $\mathcal{N}=6$ superconformal Chern-Simons matter theory known as the ABJ theory. We discuss how the parameters in the ABJ theory should be related to the bulk coupling constant in the Vasiliev theory. For this purpose, we compute two-point function of stress tensor in the ABJ theory by using supersymmmetry localization. Our result justifies the proposal by arXiv:1504.00365 and determine the unknown coefficient in the previous work.

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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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arXiv2015

Interpolating function and Stokes Phenomena

When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional $φ^4$ theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.

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arXiv2015

Supersymmetric index on T^2 x S^2 and elliptic genus

We study partition function of four-dimensional $\mathcal{N}=1$ supersymmetric field theory on $T^2 \times S^2$. By applying supersymmetry localization, we show that the $T^2 \times S^2$ partition function is given by elliptic genus of certain two-dimensional $\mathcal{N}=(0,2)$ theory. As an application, we discuss a relation between 4d Seiberg duality duality and 2d $(0,2)$ triality, proposed by Gadde, Gukov and Putrov. In other examples, we identify 4d theories giving elliptic genera of K3, M-strings and E-strings. In the example of K3, we find that there are two 4d theories giving the elliptic genus of K3. This would imply new four-dimensional duality.

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arXiv2014

On Perturbation theory improved by Strong coupling expansion

In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function consistent with the both expansions, which includes the standard Padé approximant and fractional power of polynomial method constructed by Sen as special cases. We point out that we can construct enormous number of such interpolating functions in principle while the "best" approximation for the exact answer of the physical quantity should be unique among the interpolating functions. We propose a criterion to determine the "best" interpolating function, which is applicable except some situations even if we do not know the exact answer. It turns out that our criterion works for various examples including specific heat in two-dimensional Ising model, average plaquette in four-dimensional SU(3) pure Yang-Mills theory on lattice and free energy in c=1 string theory at self-dual radius. We also mention possible applications of the interpolating functions to system with phase transition.

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arXiv2014

Higgs branch localization of 3d N=2 theories

We study N=2 supersymmetric gauge theories on squashed 3-sphere and S^1xS^2. Recent studies have shown that the partition functions in a class of N=2 theories have factorized forms in terms of vortex and anti-vortex partition functions by explicitly evaluating matrix integrals obtained from Coulomb branch localization. We directly derive this structure by performing Higgs branch localization. It turns out that more general N=2 theories have this factorization property. We also discuss the factorization of supersymmetric Wilson loop.

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