arXiv subjects

Sanefumi Moriyama

Publications and source records attributed to Sanefumi Moriyama.

At least 37 records · Page 2Linked to original sources

arXiv2017

Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings

In the so-called (2,2) theory, which is the U(N)^4 circular quiver superconformal Chern-Simons theory with levels (k,0,-k,0), it was known that the instanton effects are described by the free energy of topological strings whose Gopakumar-Vafa invariants coincide with those of the local D_5 del Pezzo geometry. By considering two types of one-parameter rank deformations U(N) x U(N+M) x U(N+2M) x U(N+M) and U(N+M) x U(N) x U(N+M) x U(N), we classify the known diagonal BPS indices by degrees. Together with other two types of one-parameter deformations, we further propose the topological string expression when both of the above two deformations are turned on.

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arXiv2016

Dualities in ABJM Matrix Model from Closed String Viewpoint

We propose a new formalism to study the ABJM matrix model. Contrary to expressing the fractional brane background with the Wilson loops in the open string formalism, we formulate the Wilson loop expectation value from the viewpoint of the closed string background. With this new formalism, we can prove some duality relations in the matrix model.

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arXiv2016

Orientifold ABJM Matrix Model: Chiral Projections and Worldsheet Instantons

We study the partition function of the orientifold ABJM theory, which is a superconformal Chern-Simons theory associated with the orthosymplectic supergroup. We find that the partition function associated with any orthosymplectic supergroup can be realized as the partition function of a Fermi gas system whose density matrix is identical to that associated with the corresponding unitary supergroup with a projection to the even or odd chirality. Furthermore we propose an identity which gives directly all of the Gopakumar-Vafa invariants for the worldsheet instanton effects in the chirally projected theories.

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arXiv2016

Prospects of the Nambu Bracket

We review recent progress in formulating the worldvolume theory of M2-branes using the Nambu bracket. Although it is generally agreed that this formulation should be replaced by another using the superconformal Chern-Simons theory, we try to pursue a possible complementary role played by the Nambu bracket. Since the partition function of the superconformal Chern-Simons theory implies a hidden super gauge group, we study the supersymmetric generalization of the Nambu bracket. We explicitly construct the superunitary Nambu algebra.

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arXiv2016

Instanton Effects in Orientifold ABJM Theory

We investigate another supersymmetric Chern-Simons theory called the orientifold ABJM theory, which replaces the unitary supergroup structure of the ABJM theory with an orthosymplectic one. Its non-perturbative structure is completely clarified by considering the duplication of the quiver.

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arXiv2016

Giambelli Identity in Super Chern-Simons Matrix Model

A classical identity due to Giambelli in representation theory states that the character in any representation is expressed as a determinant whose components are characters in the hook representation constructed from all the combinations of the arm and leg lengths of the original representation. Previously it was shown that the identity persists in taking, for each character, the matrix integration in the super Chern-Simons matrix model in the grand canonical ensemble. We prove here that this Giambelli compatibility still holds in the deformation of the fractional-brane background.

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arXiv2016

Orthosymplectic Chern-Simons Matrix Model and Chirality Projection

Recently it was found that the density matrix for a certain orthosymplectic Chern-Simons theory matches with that for the ABJM theory with the odd chiral projection. We prove this fact for a general case with the inclusion of fractional branes. We also identify the first few diagonal Gopakumar-Vafa invariants for the grand potential constructed from the chirally projected density matrix.

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arXiv2015

Exact Instanton Expansion of ABJM Partition Function

We review recent progress in determining the partition function of the ABJM theory in the large N expansion, including all of the perturbative and non-perturbative corrections. Especially, we will focus on how these exact expansions are obtained from various beautiful relations to Fermi gas system, topological string theory, integrable model and supergroup.

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arXiv2015

Superconformal Chern-Simons Partition Functions of Affine D-type Quiver from Fermi Gas

We consider the partition function of the superconformal Chern-Simons theories with the quiver diagram being the affine D-type Dynkin diagram. Rewriting the partition function into that of a Fermi gas system, we show that the perturbative expansions in 1/N are summed up to an Airy function, as in the ABJM theory or more generally the theories of the affine A-type quiver. As a corollary, this provides a proof for the previous proposal in the large N limit. For special values of the Chern-Simons levels, we further identify three species of the membrane instantons and also conjecture an exact expression of the overall constant, which corresponds to the constant map in the topological string theory.

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arXiv2015

Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings

It was known that the ABJM matrix model is dual to the topological string theory on a Calabi-Yau manifold. Using this relation it was possible to write down the exact instanton expansion of the partition function of the ABJM matrix model. The expression consists of a universal function constructed from the free energy of the refined topological string theory with an overall topological invariant characterizing the Calabi-Yau manifold. In this paper we explore two other superconformal Chern-Simons theories of the circular quiver type. We find that the partition function of one theory enjoys the same expression from the refined topological string theory as the ABJM matrix model with different topological invariants while that of the other is more general. We also observe an unexpected relation between these two theories.

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arXiv2015

ABJM Membrane Instanton from Pole Cancellation Mechanism

The coefficients of the membrane instantons in the ABJM theory are known to be quadratic polynomials of the chemical potential. We show that, after deforming the ABJM theory into more general superconformal Chern-Simons theories labelled by (q,p) where the original ABJM theory corresponds to (q,p)=(1,1), we can decompose the membrane instanton into three types of non-perturbative effects with constant coefficients independent of the chemical potential. We find that, although these constants contain poles at certain values of q and p including the ABJM case, all of the poles cancel among themselves and the finite quadratic polynomial coefficients are reproduced at these values. This is similar to what happens between the membrane instantons and the worldsheet instantons in the ABJM theory.

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arXiv2014

Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach

We study the partition function of three-dimensional ${\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which are natural generalizations of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function sums up to the Airy function as $Z(N)=e^{A}C^{-1/3}\mathrm{Ai}[C^{-1/3}(N-B)]$ with coefficients $C$, $B$ and $A$ and that for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of $B$ for general ${\mathcal N}=4$ theories, a conjectural form of $A$ for a special class of theories, and cancellation in the non-perturbative coefficients for the simplest theory next to the ABJM theory.

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arXiv2014

Instanton Effects in Orbifold ABJM Theory

We study the partition function of the orbifold ABJM theory on $S^3$, which is the $\mathcal{N}=4$ necklace quiver Chern-Simons-matter theory with alternating levels, in the Fermi gas formalism. We find that the grand potential of the orbifold ABJM theory is expressed explicitly in terms of that of the ABJM theory. As shown previously, the ABJM grand potential consists of the naive but primary non-oscillatory term and the subsidiary infinitely-replicated oscillatory terms. We find that the subsidiary oscillatory terms of the ABJM theory actually give a non-oscillatory primary term of the orbifold ABJM theory. Also, interestingly, the perturbative part in the ABJM theory results in a novel instanton contribution in the orbifold theory. We also present a physical interpretation for the non-perturbative instanton effects.

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arXiv2014

ABJ Fractional Brane from ABJM Wilson Loop

We present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop operator in the corresponding ABJM matrix model. Using this formalism, we study the phase part of the ABJ partition function numerically and find a simple expression for it. We further compute a few exact values of the partition function at some coupling constants. Fitting these exact values against the expected form of the grand potential, we can determine the grand potential with exact coefficients. The results at various coupling constants enable us to conjecture an explicit form of the grand potential for general coupling constants. The part of the conjectured grand potential from the perturbative sum, worldsheet instantons and bound states is regarded as a natural generalization of that in the ABJM matrix model, though the membrane instanton part contains a new contribution.

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arXiv2013

ABJM Wilson Loops in Arbitrary Representations

We study vacuum expectation values (VEVs) of circular half BPS Wilson loops in arbitrary representations in ABJM theory. We find that those in hook representations are reduced to elementary integrations thanks to the Fermi gas formalism, which are accessible from the numerical studies similar to the partition function in the previous studies. For non-hook representations, we show that the VEVs in the grand canonical formalism can be exactly expressed as determinants of those in the hook representations. Using these facts, we can study the instanton effects of the VEVs in various representations. Our results are consistent with the worldsheet instanton effects studied from the topological string and a prescription to include the membrane instanton effects by shifting the chemical potential, which has been successful for the partition function.

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arXiv2013

Non-perturbative effects and the refined topological string

The partition function of ABJM theory on the three-sphere has non-perturbative corrections due to membrane instantons in the M-theory dual. We show that the full series of membrane instanton corrections is completely determined by the refined topological string on the Calabi-Yau manifold known as local P1xP1, in the Nekrasov-Shatashvili limit. Our result can be interpreted as a first-principles derivation of the full series of non-perturbative effects for the closed topological string on this Calabi-Yau background. Based on this, we make a proposal for the non-perturbative free energy of topological strings on general, local Calabi-Yau manifolds.

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arXiv2013

Instanton Bound States in ABJM Theory

The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.

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arXiv2012

Instanton Effects in ABJM Theory from Fermi Gas Approach

We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1,2,3,4,6 up to N=44,20,18,16,14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.

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