# Topologically twisted N = (2, 2) supersymmetric Yang–Mills theory on an arbitrary discretized Riemann surface

@article{Matsuura2014TopologicallyTN, title={Topologically twisted N = (2, 2) supersymmetric Yang–Mills theory on an arbitrary discretized Riemann surface}, author={So Matsuura and Tatsuhiro Misumi and Kazutoshi Ohta}, journal={Progress of Theoretical and Experimental Physics}, year={2014}, volume={2014} }

We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface Σg with genus g emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes topologically twisted N = (2, 2) supersymmetric Yang-Mills theory on Σg. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino’s lattice model…

## 16 Citations

### Supersymmetric Gauge Theory on the Graph

- Mathematics
- 2021

We consider two-dimensional N =(2 , 2) supersymmetric gauge theory on discretized Riemann surfaces. We ﬁnd that the discretized theory can be eﬃciently described by using graph theory, where the…

### Exact Results in Discretized Gauge Theories

- Physics
- 2014

We apply the localization technique to topologically twisted N=(2,2) supersymmetric gauge theory on a discretized Riemann surface (the generalized Sugino model). We exactly evaluate the partition…

### Anomaly and sign problem in N = (2, 2) SYM on polyhedra: Numerical analysis

- Computer Science
- 2016

A novel phase-quench method called "anomaly-phase-quenched approximation" with respect to the $U(1)_A$ anomaly is proposed and the Ward-Takahashi (WT) identity associated with the remaining supersymmetry is realized by adopting this approximation.

### Mass spectrum of 2-dimensional N=22$$ \mathcal{N}=\left(2,2\right) $$ super Yang-Mills theory on the lattice

- PhysicsJournal of High Energy Physics
- 2019

A bstractIn the present work we analyse N=22$$ \mathcal{N}=\left(2,2\right) $$ supersymmetric Yang-Mills (SYM) theory with gauge group SU(2) in two dimensions by means of lattice simulations. The…

### Fe b 20 18 YITP-1757 O ( a ) Improvement of 2 D N = ( 2 , 2 ) Lattice SYM Theory

- Physics
- 2018

We perform a tree-level O(a) improvement of two-dimensional N = (2, 2) supersymmetric Yang-Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement…

### Numerical Analysis of Discretized ${\cal N}=(2,2)$ SYM on Polyhedra

- Computer Science
- 2016

A new phase-quenched approximation is proposed, which is called the "anomaly-phase- quenched (APQ) method", to make the partition function and observables well-defined by $U(1)_{A}$ phase cancellation.

### Topological Twists of Supersymmetric Algebras of Observables

- MathematicsCommunications in Mathematical Physics
- 2019

We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with a choice of a…

### Topological Twists of Supersymmetric Algebras of Observables

- MathematicsCommunications in Mathematical Physics
- 2019

We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with a choice of a…

### Topological twists of supersymmetric observables

- Mathematics
- 2018

We explain how to perform topological twisting of supersymmetric field theories in the language of factorization algebras. Namely, given a supersymmetric factorization algebra with a choice of a…

## References

SHOWING 1-10 OF 57 REFERENCES

### Twisted supersymmetries in lattice N = 4 super Yang-Mills theory

- Physics
- 2013

Recently it has been shown how a topologically twisted version of N = 4 super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero lattice spacing. The…

### Twisted supersymmetries in lattice $ \mathcal{N} $ = 4 super Yang-Mills theory

- Physics
- 2013

A bstractRecently it has been shown how a topologically twisted version of $ \mathcal{N} $ = 4 super Yang-Mills may be discretized in such a way as to preserve one scalar supersymmetry at nonzero…

### Lattice supersymmetry and topological field theory

- Physics
- 2003

It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this…

### N=4 supersymmetry on a space-time lattice

- Physics
- 2014

Maximally supersymmetric Yang--Mills theory in four dimensions can be formulated on a space-time lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice…

### Various super Yang-Mills theories with exact supersymmetry on the lattice

- Physics
- 2005

We continue to construct lattice super Yang-Mills theories along the line discussed in the previous papers [1,2]. In our construction of = 2, 4 theories in four dimensions, the problem of degenerate…

### Lattice study of two-dimensional N=(2,2) super Yang-Mills theory at large N

- Mathematics
- 2009

We study two-dimensional $\mathcal{N}=(2,2)$ $SU(N)$ super Yang-Mills theory on Euclidean two-torus using Sugino's lattice regularization. We perform the Monte Carlo simulation for $N=2,3,4,5$ and…

### Two-dimensional = (2, 2) supersymmetric lattice gauge theory with matter fields in the fundamental representation

- Mathematics
- 2008

In this paper, we construct a lattice formulation for two-dimensional = (2, 2) supersymmetric gauge theory with matter fields in the fundamental representation. We first construct it by the…