2
votes
1answer
107 views

What exactly is a gauge anomaly?

In lots of papers I read about gauge anomalies. For example, avoiding gauge anamolies in the MSSM is the reason for introducing an extra Higgs doublet. Gauge anamolies in the Standard Model are ...
2
votes
0answers
36 views

Twisted supermultiplets

What is a twisted supermultiplet, in a generic supersymmetric theory? Which ordinary fields belong to one of such twisted supermultiplets? I am confident with the idea of a supermultiplet or a ...
1
vote
0answers
47 views

Dual photon in d=3

In some papers (such as http://arxiv.org/abs/hep-th/9910184 and http://arxiv.org/find/all/1/all:+AND+kapustin+AND+topological+disorder/0/1/0/all/0/1) I am reading it is always referred at "the dual ...
3
votes
0answers
52 views

$\mathcal{N}=4$ SUSY in $d=3$ versus $\mathcal{N}=2$ in $d=4$

Which is the field content of the hypermultiplet and the vector multiplet in $\mathcal{N}=4 \ d=3$ Supersymmmetry? Is it correct to state that $\mathcal{N}=4$ in $d=3$ has $8$ supercharges, (since ...
2
votes
1answer
113 views

How to get a $\mathcal{N}=2$ SuperYang-Mills Lagrangian from a quiver

How can one write down the $\mathcal{N}=2$ SuperYang-Mills Lagrangian given a quiver graph? For concreteness consider the quiver $$(2)-(4)-[6]$$ where the node $(2)$ corresponds to a $U(2)$ factor ...
3
votes
0answers
107 views

Moduli Space of $\mathcal{N}=4$ SYM on $\mathbb{R} \times S^3$

When we define $\mathcal{N}=4$ SYM on flat Minkowski space, the supersymmetric vacua are parametrized by scalars living in the cartan subalgebra of the gauge group. A generic point in the moduli space ...
6
votes
2answers
178 views

How does a SCFT avoid the Haag-Lopuszanski-Sohnius theorem?

According to the Haag-Lopuszanski-Sohnius theorem the most general symmetry that a consistent 4 dimensional field theory can enjoy is supersymmery, seen as an extension of Poincarè symmetry, in direct ...
3
votes
1answer
108 views

Hyperkahler manifolds and their use in theoretical physics

Just as the title says: What is the easiest definition of a Hyperkahler Manifold? Could you give some examples of Hyperkahler manifolds, and manifolds which fail to be hyperkahler? Why are such ...
3
votes
0answers
95 views

Why does global supersymmetry commute with gauge transformations?

In particular, I would like to understand the following quotation from a paper by Witten: Nucl.Phys. B188 (1981) 513 (p. 515 at the top) His statement: This is so because in global supersymmetry ...
9
votes
2answers
276 views

Obtaining supergravity from gauging global supersymmetry

On page 92, my still favorite supersymmetry book says, by making the global infinitisimal parameter of a SUSY tranformation spacetitime dependent (gauging) it forces one to introduce a new gauge field ...
5
votes
1answer
94 views

4D instantons and the moduli space of N=2 on R^3 x S^1

I am reading the paper arXiv:0807.4723 by Gaiotto, Moore, and Neitzke on wall-crossing. I would like to understand whether if the Darboux coordinates in the mutually non-local case contain the ...
5
votes
1answer
160 views

Quantum master equation in the Batalin-Vilkovisky formalism

I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift $\delta\Psi[\chi]$ in $\Psi[\chi]$, we have $$ \begin{split} \delta ...
3
votes
0answers
49 views

Holomorphic coupling as a source for gaugino condensation

On the top of page 23 of hep-th/03061119, it is pointed out that treating the holomorphic gauge coupling $\tau$ as a background (spurion) superfield allows one to think of its $F$-term, $F_\tau$ as ...
5
votes
0answers
86 views

sigma model on $S^1 \times S^3$

In arXiv:1207.3497 - 4D partition function on $S^1 \times S^3$ and 2D Yang-Mills with nonzero area, Yuji Tachikawa explains the partition function for an 4d $\mathcal{N}=2$ sigma model on $S^3 \times ...
7
votes
0answers
136 views

How to perform contour integral in Nekrasov's formula

My question is technical. It is about instanton counting calculation (see this paper). The partition function of SU(N) gauge theory with $N_f$ fundamental multiplets in k instanton background is ...
2
votes
1answer
176 views

Construction of the supersymmetric Faraday tensor

When I first learned gauge theories in my introductory quantum field theory course, I was taught that the Faraday (field-strength) tensor can be constructed by computing the commutator of the ...
2
votes
1answer
449 views

Wilson loops and gauge invariant operators (Part 1)

I guess the Hilbert space of the theory is precisely the space of all gauge invariant operators (mod equations of motion..as pointed out in the answers) Is it possible that in a gauge theory the ...
6
votes
4answers
983 views

What's the distinctions between Yang-Mills theory and QCD?

So Yang-Mills theory is a non-abelian gauge theory, and we used a lot in QCD calculation. But what are the distinctions between Yang-Mills theory and QCD? And distinctions between supersymmetric ...
30
votes
0answers
1k views

On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $\mathcal N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the ...
8
votes
2answers
329 views

How to prove quantum N=4 Super-Yang-Mills is superconformal?

I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations Also, does a non-perturbative proof exist?
12
votes
2answers
335 views

Topological twists of SUSY gauge theory

Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this theory has 3 ...
9
votes
1answer
48 views

Dual Pairs in Four Dimensions

Following the conversation here, I am wondering if anyone knows of an example of dual pair with 4-dimensional N=1 SUSY which relates a non-Abelian gauge theory on one side to a theory with a ...