A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. ...

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30
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827 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 ...
22
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0answers
183 views

Systematic approach to deriving equations of collective field theory to any order

The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
9
votes
0answers
542 views

Gauge redundancies and global symmetries

It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
8
votes
0answers
177 views

How does the Super-Kamiokande experiment falsify SU(5)?

In his book "The Trouble With Physics", Lee Smolin writes that he is still stunned by the falsification of the $SU(5)$ Georgi-Glashow model by the null results of proton decay experiments. I should ...
8
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0answers
124 views

Gauge fields in Polyakov's treatment of renormalization for nonlinear sigma model

I am deriving the results of renormalization for nonlinear sigma model using Polyakov approach. I am closely following chapter 2 of Polyakov's book--- ``Gauge fields and strings''. Action for the ...
7
votes
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130 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 ...
6
votes
0answers
85 views

Does the inverse of the Dirac conjecture hold?

In the theory of constrained Hamiltonian systems, one differentiates between primary and secondary constraints, where the former are constraints derived directly from the Hamiltonian in question and ...
6
votes
0answers
211 views

Is the U(1) gauge theory in 2+1D dual to a U(1) or an integer XY model?

The compact U(1) lattice gauge theory is described by the action $$S_0=-\frac{1}{g^2}\sum_\square \cos\left(\sum_{l\in\partial \square}A_l\right),$$ where the gauge connection $A_l\in$U(1) is defined ...
5
votes
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91 views

Non abelian gauge theory with charged scalar field

Suppose we have an SU(N) non abelian gauge theory coupled with a multiplet of complex scalar fields $\Phi$. The lagrangian would be $$ L= - \frac 12 \text{Tr } F_{\mu\nu}F^{\mu\nu} + |D_\mu \Phi|^2 - ...
5
votes
0answers
67 views

The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
5
votes
0answers
60 views

axial and vector resonances in composite higgs models

Is there a reason to believe that the axial resonances be heavier than the vector resonances in the composite higgs models? For instance, in http://arxiv.org/abs/0808.2071, to have zero tree level ...
5
votes
0answers
77 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 ...
5
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0answers
123 views

Master Field Large N limit

I would like to ask a question about the so-called ''Master Field''. As far as I understand, this represents a classical configuration in the large n limit (saddle point solution) but there is no ...
5
votes
0answers
131 views

Gauge-invariance of pole mass using Ward Identity

I am able to explicitly verify to one-loop order that pole masses are independent of the choice of gauge paramter. But how do I use the Ward-Identity/Taylor-Slavnov identity show that the position of ...
5
votes
0answers
211 views

7 sphere, is there any physical interpretation of exotic spheres?

Basically an exotic sphere is topologically a sphere, but doesn't look like a one. Or more accurately: homeomorphic but not diffeomorphic to the standard Euclidean n-sphere The first exotic ...
5
votes
0answers
82 views

How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer?

How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer? There are some gauges with negative norms. It's true that if restricted to gauge invariant states, the ...
4
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0answers
67 views

Unitary gauge for non-abelian case

I'm reading Chapter 19 of Mandle and Shaw's Quantum field theory. In the first section it is explained that one can go with a $SU(2)$ followed by a $U(1)$ transformation from ...
4
votes
0answers
77 views

(coordinates) Invariance/Covariance of Chern-Simons theory and Yang-Mills theory

It is known that 3D Chern-Simons(C-S) theory has no explicit metric involving in the Lagrangian density: $$ A \wedge dA + (2/3) A \wedge A \wedge A $$ while the 4D Yang-Mills(Y-M) theory has the ...
4
votes
0answers
100 views

Noether current for the Lagrangian without Lorentz invariance

I am reading an article by Watanabe & Murayama. It gives a proof on the counting of Nambu–Goldstone bosons without Lorentz invariance. I am trying to derive all the equations to get a better ...
4
votes
0answers
400 views

The meaning of Goldstone boson equivalence theorem

The Goldstone boson equivalence theorem tells us that the amplitude for emission/absorption of a longitudinally polarized gauge boson is equal to the amplitude for emission/absorption of the ...
4
votes
0answers
346 views

Gauge invariance and Feynman path-integrals

Let me look at the Hamiltonian of a charged particle in a plane in a constant magnetic field ($\vec{B}$) pointing upwards - then in usual notation it is, $$\hat{H} = \frac{1}{2m}\biggl(\hat{p} + ...
3
votes
0answers
52 views

Complex scalar fields conserved charges

I'm currently studying field theory and I'm having some trouble with conserved charge given in field components. If we have a complex scalar action of a field $\phi=(\phi_1,\phi_2)^T$ that is ...
3
votes
0answers
33 views

Quiver and Gauge theory

i want to know how to construct a quiver of a Gauge theory specified by groupe g with rank=r ?
3
votes
0answers
65 views

Large gauge transformations for higher p-form gauge fields

Question: What is the large gauge transformations for higher p-form gauge field on a spatial d-dimensional torus $T^d$ or a generic (compact) manifold $M$? for p=1,2,3, etc or any other integers. Is ...
3
votes
0answers
123 views

Does the projected spin state of the $d+id$ mean-field Hamiltonian on a triangular lattice has time-reversal(TR) symmetry?

Consider the following $d+id$ mean-field Hamiltonian for a spin-1/2 model on a triangular lattice $$H=\sum_{<ij>}(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$$, with $\chi_{ij}=\begin{pmatrix} 0 & ...
3
votes
0answers
44 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 ...
3
votes
0answers
78 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 ...
3
votes
0answers
58 views

Do primary first class constraints change the electric field in the Hamiltonian form of Maxwell's theory?

In my understanding of Dirac's theory of constrained Hamiltonians, the primary (and also the secondary) first class constraints are generators of canonical transformations that do not change the ...
3
votes
0answers
84 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 ...
3
votes
0answers
66 views

Is there a critical order of the Abelian gauge theory in (2+1)D

In (2+1)D spacetime, it is known that the $U(1)$ gauge theory is always confined (according to Polyakov), while the $\mathbb{Z}_2$ gauge theory can support a deconfined phase. Now consider a generic ...
3
votes
0answers
68 views

Does the ensemble of effective Lagrangians in the String theory landscape mostly include gauge theories?

String theory false vacua can be described by effective Lagrangians at low energy. Is there generally a correspondence between these effective Lagrangians and SU(N) gauge theories? Or do the effective ...
3
votes
0answers
163 views

Pseudo scalar mass and Pure scalar mass

Since the only difference between pseudo scalar and a scalar term is just a change of sign under a parity inversion, is it possible that both of them be present in the same field and interact? For ...
3
votes
0answers
125 views

Derivation of the enhancement of U(1)$_L$ x U(1)$_R$ to SU(2)$_L$ x SU(2)$_R$ at the self-dual radius

Towards the end of the paragraph with the title String theory's added value 2: enhanced non-Abelian symmetries at self-dual radii and abstract C with current algebras of this article, it is explained ...
3
votes
0answers
177 views

Attempts to explain Higgs coupling as a gauge transformation symmetry

As is (supposedly) well known, Electromagnetic coupling can be "explained" as a closure term to a langrangian comprising a free Dirac field and a free vector field that are required to be invariant ...
2
votes
0answers
44 views

A question about the constraints in BRST-Fock theories

In BRST Symmetry in the Classical and Quantum Theories of Gauge Systems, Henneaux says the Fock representation is not applicable to an odd number of constraints. Then he goes on to say that the ...
2
votes
0answers
32 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 ...
2
votes
0answers
36 views

Degeneracy and the unitarity of a gauge theory with a non-compact gauge group

The topological ground state degeneracy(g.s.d.) provides useful information for a topological field theory(TQFT), such as this post shows some example. To count g.s.d., it seems to be equivalent to ...
2
votes
0answers
38 views

What's the necessary and sufficient condition for gauge equivalence in the projective construction?

The definition of gauge equivalence and notations used here is the same as those in my previous question. As we know, the condition $\chi_{ij}'=G_i\chi_{ij}G_j^\dagger$(where $G_i\in SU(2)$) is a ...
2
votes
0answers
73 views

Some questions on the Wilson loop in the projective construction?

Based on the previous question and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij}'\psi_j+H.c.)$, we ...
2
votes
0answers
106 views

Is the $SU(2)$ flux defined in the context of Projective Symmetry Group(PSG) an observable quantity?

The $SU(2)$ flux defined in the context of PSG is as follows: Consider the mean-field Hamiltonian $H_{MF}=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ description of a 2D lattice spin-model, the ...
2
votes
0answers
88 views

From Berry's phase to artificial Gauge potential

How a nonzero geometric phase in a loop is used to generate artificial gauge potentials? If possible, also discuss how to generate the non-abelian artificial gauge potentials.
2
votes
0answers
44 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 ...
2
votes
0answers
37 views

What is the physical meaning of the higher order structure functions in the BRST quantization of open algebras?

What is the physical meaning of the higher order structure functions in the BRST quantization of open algebras? As opposed to formal algebraic manipulations. Thanks.
1
vote
0answers
38 views

General covariance and global Poincaré algebras

Reading an article (page 7) I read this: Just as ordinary general covariance may be regarded as the local gauge symmetry corresponding to the global Poincare algebra and local gauge invariance ...
1
vote
0answers
48 views

Inverse of gauge covariant derivative

Consider the gauge covariant derivative defined by $$ D_z = d_z + \Delta_z $$ or explicitly $$ (D_z)^a{}_c = \delta^a_c d_z + (\Delta_z)^a{}_c = \delta^a_c d_z + f_{bc}{}^a A_z^b $$ Here, $d_z$ is the ...
1
vote
0answers
47 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
1
vote
0answers
45 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 ...
1
vote
0answers
55 views

Why is the following gauge transformation singular?

Suppose I have a single particle Hamiltonian: $H=\frac{p^2}{2m}+\frac{\hbar k_0}{m}\vec{\sigma}\cdot\vec{p}$, either for boson or fermion. I do a gauge transformation ...
1
vote
0answers
40 views

Some question on the definition of flux in the projective construction?

Here I have some confusing points about the definition of flux in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ ...
1
vote
0answers
57 views

Do Boundary Conditions depend on spin connections for gauge fields?

In the article arXiv:1206.5642, which talks about gauge fields in conical spacetime, I came across the statement in footnote 4 that the boundary conditions on the gauge field depend on the spin ...