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So Matsuura

Publications and source records attributed to So Matsuura.

At least 37 records · Page 2Linked to original sources
arXiv2012

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N = 2 U(k) SYM on R^2 x (Fuzzy R^2) around the minimum of k-coincident fuzzy spheres.

hep-lat↗
arXiv2011

Recent progress of lattice and non-lattice super Yang-Mills

We report recent progress of non-perturbative formulation of supersymmetric Yang-Mills. Although lattice formulations of two-dimensional theories which are fine tuning free to all order in perturbation theory are known for almost ten years, however, there were only few evidence for the validity at non-perturbative level. In this talk we argue that most numerical studies so far do not capture the physics in continuum, and add new evidence that lattice formulation works at non-perturbatively. We further point out that, by combining two-dimensional lattice and matrix model techniques inspired by D-brane dynamics in superstring theory, a non-perturbative formulation of the four-dimensional maximally supersymmetric Yang-Mills theory, which is free from the fine tuning at least to all order in perturbation theory, is obtained.

hep-lat↗
arXiv2011

Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills

We construct a lattice formulation of a mass-deformed two-dimensional N=(8,8) super Yang-Mills theory with preserving two supercharges exactly. Gauge fields are represented by compact unitary link variables, and the exact supercharges on the lattice are nilpotent up to gauge transformations and SU(2)_R rotations. Due to the mass deformation, the lattice model is free from the vacuum degeneracy problem, which was encountered in earlier approaches, and flat directions of scalar fields are stabilized giving discrete minima representing fuzzy S^2. Around the trivial minimum, quantum continuum theory is obtained with no tuning, which serves a nonperturbative construction of the IIA matrix string theory. Moreover, around the minimum of k-coincident fuzzy spheres, four-dimensional N=4 U(k) super Yang-Mills theory with two commutative and two noncommutative directions emerges. In this theory, sixteen supersymmetries are broken by the mass deformation to two. Assuming the breaking is soft, we give a scenario leading to undeformed N=4 super Yang-Mills on R^4 without any fine tuning. As an evidence for the validity of the assumption, some computation of 1-loop radiative corrections is presented.

hep-lat↗
arXiv2011

Nonperturbative studies of supersymmetric matrix quantum mechanics with 4 and 8 supercharges at finite temperature

We investigate thermodynamic properties of one-dimensional U(N) supersymmetric gauge theories with 4 and 8 supercharges in the planar large-N limit by Monte Carlo calculations. Unlike the 16 supercharge case, the threshold bound state with zero energy is widely believed not to exist in these models. This led A.V. Smilga to conjecture that the internal energy decreases exponentially at low temperature instead of decreasing with a power law. In the 16 supercharge case, the latter behavior was predicted from the dual black 0-brane geometry and confirmed recently by Monte Carlo calculations. Our results for the models with 4 and 8 supercharges indeed support the exponential behavior, revealing a qualitative difference from the 16 supercharge case.

hep-th↗
arXiv2008

Instanton Counting and Dielectric Branes

We consider the Hanany-Witten type brane configuration in a background of RR 4-form field strength and examine the behavior of Euclidean D0-branes propagating between two NS5-branes. We evaluate the partition function of the D0-branes and show that it coincides with the Nekrasov partition function of instantons for four-dimensional N=2 supersymmetric Yang-Mills theory. In this analysis, the Myers effect plays a crucial role. We apply the same method to the brane configuration realizing four-dimensional N=2 theory with hypermultiplets in the fundamental representation and reproduce the corresponding Nekrasov partition function.

hep-th↗
arXiv2008

Two-dimensional N=(2,2) Supersymmetric Lattice Gauge Theory with Matter Fields in the Fundamental Representation

In this paper, we construct a lattice formulation for two-dimensional N=(2,2) supersymmetric gauge theory with matter fields in the fundamental representation. We first construct it by the orbifolding procedure from Yang-Mills matrix theory with eight supercharges. We show that we can obtain the same lattice formulation by extending the geometrical discretization scheme. This suggests that the equivalence between the two schemes holds even for theories with matter fields.

hep-th↗
arXiv2008

Geometry of Orbifolded Supersymmetric Lattice Gauge Theories

We prove that the prescription for construction of supersymmetric lattice gauge theories by orbifolding and deconstruction directly leads to Catterall's geometrical discretization scheme in general. These two prescriptions always give the same lattice discretizations when applied to theories of p-form fields. We also show that the geometrical discretization scheme can be applied to more general theories.

hep-th↗
arXiv2007

Exact Vacuum Energy of Orbifold Lattice Theories

We investigate the orbifold lattice theories constructed from supersymmetric Yang-Mills matrix theories (mother theories) with four and eight supercharges. We show that the vacuum energy of these theories does not receive any quantum correction perturbatively.

hep-lat↗
arXiv2007

Classification of Supersymmetric Lattice Gauge Theories by Orbifolding

We provide a general classification of supersymmetric lattice gauge theories that can be obtained from orbifolding of theories with four and eight supercharges. We impose at least one preserved supercharge on the lattice and Lorentz invariance in the naive continuum limit. Starting with four supercharges, we obtain one two-dimensional lattice gauge theory, identical to the one already given in the literature. Starting with eight supercharges, we obtain a unique three-dimensional lattice gauge theory and infinitely many two-dimensional lattice theories. They can be classified according to seven distinct groups, five of which have two preserved supercharges while the others have only one.

hep-lat↗
arXiv2007

Relations among Supersymmetric Lattice Gauge Theories via Orbifolding

We show how to derive Catterall's supersymmetric lattice gauge theories directly from the general principle of orbifolding followed by a variant of the usual deconstruction. These theories are forced to be complexified due to a clash between charge assignments under U(1)-symmetries and lattice assignments in terms of scalar, vector and tensor components for the fermions. Other prescriptions for how to discretize the theory follow automatically by orbifolding and deconstruction. We find that Catterall's complexified model for the two-dimensional N=(2,2) theory has two independent preserved supersymmetries. We comment on consistent truncations to lattice theories without this complexification and with the correct continuum limit. The construction of lattice theories this way is general, and can be used to derive new supersymmetric lattice theories through the orbifolding procedure. As an example, we apply the prescription to topologically twisted four-dimensional N=2 supersymmetric Yang-Mills theory. We show that a consistent truncation is closely related to the lattice formulation previously given by Sugino.

hep-lat↗
arXiv2006

Construction of Instantons via Tachyon Condensation

We investigate the D-brane bound states from the viewpoint of the unstable D/\bar{D}-system and their tachyon condensation. We consider two systems; a system of k D(-1)-branes and N D3-branes with open strings connecting them and a system of N D3-branes with open strings corresponding to the k-instanton flux, both of which are realized through the tachyon condensation from (N+2k) D3-branes and 2k \bar{D3}-branes with appropriate tachyon profiles. It can be shown that these systems are related with each other through a unitary gauge transformation of the D3/\bar{D3}-system. We construct an explicit form of the gauge transformation and show that the essential elements of the ADHM construction naturally arise from the explicit form of the gauge transformation. As a result, the ADHM construction is understood as an outcome of this gauge equivalence in different low energy limits. The small instanton singularities can be also understood in this context. Other kinds of solitons with different codimensions are also discussed from the view point of the tachyon condensation.

hep-th↗
arXiv2006

Localization on the D-brane, two-dimensional gauge theory and matrix models

We consider the effective topological field theory on Euclidean D-strings wrapping on a 2-cycle in the internal space. We evaluate the vev of a suitable operator corresponding to the chemical potential of vortices bounded to the D-strings, and find that it reduces to the partition function of generalized two-dimensional Yang-Mills theory as a result of localization. We argue that the partition function gives a grand canonical ensemble of multi-instanton corrections for four-dimensional N=2 gauge theory in a suitable large N limit. We find two-dimensional gauge theories that provide the instanton partition function for four-dimensional N=2 theories with the hypermultiplets in the adjoint and fundamental representations. We also propose a partition function that gives the instanton contributions to four-dimensional N=2 quiver gauge theory. We discuss the relation between Nekrasov's instanton partition function and the Dijkgraaf-Vafa theory in terms of large N phase transitions of the generalized two-dimensional Yang-Mills theory.

hep-th↗
arXiv2006

Excited D-branes and Supergravity Solutions

We investigate the general solution with the symmetry ISO(1,p)xSO(9-p) of Type II supergravity (the three-parameter solution) from the viewpoint of the superstring theory. We find that one of the three parameters (c_1) is closely related to the ``dilaton charge'' and the appearance of the dilaton charge is a consequence of deformations of the boundary condition from that of the boundary state for BPS D-branes. We give three examples of the deformed D-branes by considering the tachyon condensation from systems of D-\bar{D}p-branes, unstable D9-branes and unstable D-instantons to the BPS saturated Dp-branes, respectively. We argue that the deformed systems are generally regarded as tachyonic and/or massive excitations of the open strings on Dp-\bar{D}p-brane systems.

hep-th↗
arXiv2005

Open String Tachyon in Supergravity Solution

We study the tachyon condensation of the D-\bar{D}-brane system with a constant tachyon vev in the context of classical solutions of the Type II supergravity. We find that the general solution with the symmetry ISO(1,p)xSO(9-p) (the three-parameter solution) includes the extremal black p-brane solution as an appropriate limit of the solution with fixing one of the three parameters (c_1). Furthermore, we compare the long distance behavior of the solution with the massless modes of the closed strings from the boundary state of the D-\bar{D}-brane system with a constant tachyon vev. We find that we must fix c_1 to zero and the only two parameters are needed to express the tachyon condensation of the DD-brane system. This means that the parameter $c_1$ does not correspond to the tachyon vev of the DD-brane system.

hep-th↗
arXiv2004

String Theoretical Interpretation for Finite N Yang-Mills Theory in Two-Dimensions

We discuss the equivalence between a string theory and the two-dimensional Yang-Mills theory with SU(N) gauge group for finite N. We find a sector which can be interpreted as a sum of covering maps from closed string world-sheets to the target space, whose covering number is less than N. This gives an asymptotic expansion of 1/N whose large N limit becomes the chiral sector defined by D.Gross and W.Taylor. We also discuss that the residual part of the partition function provides the non-perturbative corrections to the perturbative expansion.

hep-th↗
arXiv2004

Large N limit of 2D Yang-Mills Theory and Instanton Counting

We examine the two-dimensional U(N) Yang-Mills theory by using the technique of random partitions. We show that the large N limit of the partition function of the 2D Yang-Mills theory on S^2 reproduces the instanton counting of 4D N=2 supersymmetric gauge theories introduced by Nekrasov. We also discuss that we can take the ``double scaling limit'' by fixing the product of the N and cell size in Young diagrams, and the effective action given by Douglas and Kazakov is naturally obtained by taking this limit. We give an interpretation for our result from the view point of the superstring theory by considering a brane configuration that realizes 4D N=2 supersymmetric gauge theories.

hep-th↗
arXiv2003

Closed String Field Theory with Dynamical D-brane

We consider a closed string field theory with an arbitrary matter current as a source of the closed string field. We find that the source must satisfy a constraint equation as a consequence of the BRST invariance of the theory. We see that it corresponds to the covariant conservation law for the matter current, and the equation of motion together with this constraint equation determines the classical behavior of both the closed string field and the matter. We then consider the boundary state (D-brane) as an example of a source. We see that the ordinary boundary state cannot be a source of the closed string field when the string coupling g turns on. By perturbative expansion, we derive a recursion relation which represents the bulk backreaction and the D-brane recoil. We also make a comment on the rolling tachyon boundary state.

hep-th↗