# Large N reduction on group manifolds

@article{Kawai2009LargeNR, title={Large N reduction on group manifolds}, author={Hikaru Kawai and Shinji Shimasaki and Asato Tsuchiya}, journal={arXiv: High Energy Physics - Theory}, year={2009} }

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S^3 can be regularized in a gauge invariant and SO(4) invariant manner.

#### 28 Citations

Large N reduction on coset spaces

- Physics
- 2010

As an extension of our previous work concerning the large N reduction on group manifolds, we study the large N reduction on coset spaces. We show that large N field theories on coset spaces are… Expand

Equivalence of large-N gauge theories on a group manifold and its coset space

- Physics
- 2018

Abstract In 2010, Kawai, Shimasaki and one of the present authors (A.T.) showed that the large-N reduction holds on group manifolds in the sense that a large-N gauge theory on a group manifold is… Expand

Hermitian generalized Jordan triple systems and certain applications to field theory

- Physics
- 2014

We define Hermitian generalized Jordan triple systems and prove a structure theorem. We also give some examples of the systems and study mathematical properties. We apply a Hermitian generalized… Expand

Gauge Theories in Noncommutative Homogeneous

- Mathematics
- 2014

We construct a gauge theory on a noncommutative homogeneous Kahler man- ifold, where we employ the deformation quantization with separation of variables for Kahler manifolds formulated by Karabegov.… Expand

Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models

- Physics
- 2012

We study reduced matrix models obtained by the dimensional reduction of N=2 quiver Chern-Simons theories on S^3 to zero dimension and show that if a reduced model is expanded around a particular… Expand

Gauge Theories in Noncommutative Homogeneous K\"ahler Manifolds

- Physics, Mathematics
- 2014

We construct a gauge theory on a noncommutative homogeneous K\"ahler manifold, where we employ the deformation quantization with separation of variables for K\"ahler manifolds formulated by… Expand

3-Algebras in String Theory

- Mathematics
- 2012

In this chapter, we review 3-algebras that appear as fundamental properties of string theory. 3-algebra is a generalization of Lie algebra; it is defined by a tri-linear bracket instead of by a… Expand

A Novel Large-N Reduction on S^3: Demonstration in Chern-Simons Theory

- Physics
- 2010

Abstract We show that the planar Chern–Simons (CS) theory on S 3 can be described by its dimensionally reduced model. This description of CS theory can be regarded as a novel large-N reduction for… Expand

Localization and Large N reduction on S^3 for the Planar and M-theory limit

- Physics
- 2012

We show a large N reduction on S3 in a BPS sector for a broad class of theories: N⩾2 supersymmetric Chern–Simons theory with any number of adjoint and bi-fundamental chiral multiplets. We show that a… Expand

Dimensional oxidization on coset space

- Physics
- 2020

In the matrix model approaches of string/M theories, one starts from a generic symmetry $gl(\infty)$ to reproduce the space-time manifold. In this paper, we consider the generalization in which the… Expand

#### References

SHOWING 1-10 OF 52 REFERENCES

Large N reduction on coset spaces

- Physics
- 2010

As an extension of our previous work concerning the large N reduction on group manifolds, we study the large N reduction on coset spaces. We show that large N field theories on coset spaces are… Expand

Large N reduction for Chern-Simons theory on S 3

- Physics
- 2009

We study a matrix model which is obtained by dimensional reduction of Chern-Simons theory on S{sup 3} to zero dimension. We find that, expanded around a particular background consisting of multiple… Expand

A simple expression for planar field theories

- Physics
- 1982

Abstract We argue that in a U ( N ) invariant theory in presence of a random background gauge field, the quenched expectation values of U ( N ) invariant objects are volume independent in the limit N… Expand

Large-N reduction in the continuum three-dimensional Yang-Mills theory.

- Physics, Medicine
- Physical review letters
- 2003

Three-dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side l=l(c) as expected of a noninteracting string theory and the situation in four dimensions is expected to be similar. Expand

Fiber Bundles and Matrix Models

- Physics
- 2008

We investigate the relationship between a gauge theory on a principal bundle and that on its base space. In the case where the principal bundle is itself a group manifold, we also study relations of… Expand

Large-N reduced models of supersymmetric quiver, Chern-Simons gauge theories and ABJM

- Physics
- 2009

Using the Eguchi-Kawai equivalence, we provide regularizations of supersymmetric quiver and Chern-Simons gauge theories which leave the supersymmetries unbroken. This allow us to study many… Expand

Four-dimensional N = 1 super Yang-Mills theory from a matrix model

- Physics
- 2009

We consider a supersymmetric matrix quantum mechanics. This is obtained by adding Myers and mass terms to the dimensional reduction of 4D N=1 super Yang-Mills theory to one dimension. Using this… Expand

A Large N reduced model as superstring

- Physics
- 1996

Abstract A matrix model which has the manifest ten-dimensional N = 2 super Poincare invariance is proposed. Interactions between BPS-saturated states are analyzed to show that the massless spectrum… Expand

N = 4 super Yang-Mills theory from the plane wave matrix model

- Physics
- 2008

We propose a nonperturbative definition of N=4 super Yang-Mills (SYM). We realize N=4 SYM on RxS{sup 3} as the theory around a vacuum of the plane wave matrix model. Our regularization preserves 16… Expand

Describing Curved Spaces by Matrices

- Physics
- 2005

It is shown that a covariant derivative on any d-dimensional manifold M can be mapped to a set of d operators acting on the space of functions defined on the principal Spin(d)-bundle over M. In other… Expand