S-duality in Vafa-Witten theory for non-simply laced gauge groups

@article{Wu2008SdualityIV,
  title={S-duality in Vafa-Witten theory for non-simply laced gauge groups},
  author={Siye Wu},
  journal={Journal of High Energy Physics},
  year={2008},
  volume={2008},
  pages={009-009}
}
  • Siye Wu
  • Published 14 February 2008
  • Mathematics
  • Journal of High Energy Physics
Vafa-Witten theory is a twisted N = 4 supersymmetric gauge theory whose partition functions are the generating functions of the Euler number of instanton moduli spaces. In this paper, we recall quantum gauge theory with discrete electric and magnetic fluxes and review the main results of Vafa-Witten theory when the gauge group is simply laced. Based on the transformations of theta functions and their appearance in the blow-up formulae, we propose explicit transformations of the partition… 

Some analytic aspects of Vafa-Witten twisted N̳ = 4 supersymmetric Yang-Millseory theory

Given an oriented Riemannian four-manifold equipped with a principal bundle, we investigate the moduli spaceMVW of solutions to the Vafa-Witten equations. ese equations arise from a twist ofN = 4

Non-orientable surfaces and electric-magnetic duality

  • Siye Wu
  • Mathematics
    Journal of High Energy Physics
  • 2018
A bstractWe consider the reduction along two compact directions of a twisted N = 4 gauge theory on a 4-dimensional orientable manifold which is not a global product of two surfaces but contains a

Phases of N = 4 SYM , S-duality and Nilpotent Cones

In this note, I describe the space of vacua V of four dimensional N = 4 SYM on R4 with gauge group a compact simple Lie Group G as a stratified space. On each stratum, the low energy effective field

M-theoretic derivations of 4d-2d dualities: from a geometric Langlands duality for surfaces, to the AGT correspondence, to integrable systems

A bstractIn part I, we extend our analysis in [arXiv:0807.1107], and show that a mathematically conjectured geometric Langlands duality for complex surfaces in [1], and its generalizations — which

Reading between the lines of four-dimensional gauge theories

A bstractStarting with a choice of a gauge group in four dimensions, there is often freedom in the choice of magnetic and dyonic line operators. Different consistent choices of these operators

Phases of $\mathcal{N}=4$ SYM, S-duality and Nilpotent Cones

In this note, I describe the space of vacua $\mathcal{V}$ of four dimensional $\mathcal{N}=4$ SYM on $\mathbb{R}^4$ with gauge group a compact simple Lie Group $G$ as a stratified space. On each

Reading between the lines of four-dimensional gauge theories

Starting with a choice of a gauge group in four dimensions, there is often freedom in the choice of magnetic and dyonic line operators. Different consistent choices of these operators correspond to

References

SHOWING 1-10 OF 51 REFERENCES

On S-duality for Non-Simply-Laced Gauge Groups

We point out that for Script N = 4 gauge theories with exceptional gauge groups G_2 and F_4 the S-duality transformation acts on the moduli space by a nontrivial involution. We note that the duality

The Vafa-Witten Theory for Gauge Group SU(N)

We derive the partition function for the Vafa-Witten twist of the $\cn=4$ supersymmetric gauge theory with gauge group SU(N) (for prime $N$) and arbitrary values of the 't Hooft fluxes $v\in

N = 4 supersymmetric Yang-Mills theory on orbifold-T4/Z2 higher rank case, 17 pages

We derive the partition function of N=4 supersymmetric Yang–Mills theory on orbifold-T4/Z2. In classical geometry, K3 surface is constructed from the orbifold-T4/Z2. Along the same way as the

Gauge Theory, Ramification, And The Geometric Langlands Program

In the gauge theory approach to the geometric Langlands program, ramification can be described in terms of "surface operators," which are supported on two-dimensional surfaces somewhat as Wilson or

Monopoles and four-manifolds

Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining

The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups

We establish a relation between the generating functions appearing in the S-duality conjecture of Vafa and Witten and geometric Eisenstein series for Kac-Moody groups. For a pair consisting of a

Miniscule representations, Gauss sum and modular invariance

After explaining the concepts of Langlands dual and miniscule representations, we define an analog of the Gauss sum for any compact, simple Lie group with a simply laced Lie algebra. We then show a
...