Questions tagged [gauge-theory]

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. Examples include the $U(1)$-symmetric quantum electrodynamics and other Yang-Mills theories wherein non-Abelian groups replace the $U(1)$ gauge group of QED.

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On the Coulomb branch of ${\cal N}=2$ supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D ${\cal N}=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs ...
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951 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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
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1k views

How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
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261 views

Do all $\mathcal{N}=2$ Gauge Theories “Descend” from String Theory?

I'm thinking about the beautiful story of "geometrical engineering" by Vafa, Hollowood, Iqbal (https://arxiv.org/abs/hep-th/0310272) where various types of $\mathcal{N}=2$ SYM gauge theories on $\...
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286 views

What is the global symmetry group associated to the C-field?

The C-field in 11-dimensional supergravity is an elusive object that is not the simple higher $\mathrm{U}(1)$-gauge field one would naively make this out to be. For an overview of possible models for ...
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702 views

Classical electrodynamics as an $\mathrm{U}(1)$ gauge theory

Preface: I haven't studied QED or any other QFT formally, only by occasionally flipping through books, and having a working knowledge of the mathematics of gauge theories (principal bundles, etc.). ...
8
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1answer
258 views

Anyon condensation – what's the precise definition?

Say I have an anyonic system modelled as a Chern-Simons system with group $G$. If the centre of $G$ is non-trivial, one may also study the system described by $G/\Gamma$, where $\Gamma$ is a discrete ...
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294 views

Is the QCD Lagrangian without a $\theta$-term invariant under large gauge transformations?

In his book "Quantum field theory", Kerson Huang states that we need to add the term $$\frac{i\theta}{32\pi^2}G_{\mu\nu}^a \tilde{G}_{\mu\nu}^a$$ to the Lagrangian, to make it invariant under large ...
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248 views

Intuition for Homological Mirror Symmetry

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
8
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156 views

Why does strong interaction increase with distance?

I read numerous times that strong interaction increases with distance. But how can one actually derive the force-distance relation from the lagrangian (quark field + gluon field + gauge coupling)? ...
8
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114 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 ...
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177 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 ...
7
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91 views

Can the Dirac quantization condition be derived within Lev Vaidman's formalism without gauge fields?

Textbooks often claim that phenomena like the Aharonov-Bohm effect require that any local formulation of quantum gauge theory use gauge potential fields. (It's also sometimes claimed that the A-B ...
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185 views

Non-abelian string in QCD?

It is easy to find various/many papers in HEP-lattice talk about "Non abelian string in QCD". What does it mean to say "non abelian string in QCD?" Does "non abelian string" happen for pure Yang-...
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265 views

$U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic? The action I am interested in is $$...
7
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108 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 ...
6
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1answer
142 views

What classifies gaugings?

Gauging a global symmetry $G$ introduces several free parameters to the theory. For example, In $d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ...
6
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222 views

Is the vacuum degenerate in the Abelian Higgs model?

Consider the theory with Lagrangian $$ \mathcal{L} = -\frac{1}{4}F_{\mu \nu} F^{\mu \nu} + (D_\mu \phi)^* (D^\mu \phi) - U(\phi) \,, $$ where $U(\phi)$ breaks the $U(1)$ symmetry of the system. If we ...
6
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220 views

Definition of gravity path integral?

In a non-abelian gauge theory there is a "fundamental" gauge field $A_\mu^a$ with gauge index $a$ often called connection. Although $ A_\mu^a$ is not gauge invariant, gauge invariant quantities can be ...
6
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1answer
132 views

How does gauge invariance protect the SM gauge boson masses in SUSY from divergent radiative corrections?

The W and Z gauge bosons receive radiative corrections in loop from the heavy SUSY scalars. There is an argument using gauge invariance which explains how the masses remains protected. I am not able ...
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217 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
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151 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 ...
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138 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 ...
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209 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
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111 views

World-volume (higher) gauge theory on D-branes

It is well known that if one constructs ordinary WZW type sigma model for string action, it is possible whenever they find a cocycle in appropriate Chevalley-Eilenberg algebra. If I understand it ...
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137 views

Is it possible to couple an odd number of Dirac fermions, at finite density, to a massless gauge field in 2+1d?

In a beautiful paper by A. N. Redlich (PRL $\bf{52}$, 18 (1984)) on the parity anomaly, the author indicates that an odd number of Dirac fermions can never be coupled to a massless gauge field in 2+1d ...
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93 views

Path integral and gauge redundancy for slave particle

In the slave boson, we have $c^\dagger = b f^\dagger$ where $b$ is boson and $f$ is fermion. There is also a local constraint $b^\dagger b+f^\dagger f=1$ to retrict the Hilbert space and a $U(1)$ ...
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295 views

Physical origin of Nekrasov Partition Function

I've seen a few papers [1,2,3,4] which defined Nekrasov Partition Function as (in particular [2,3,4]) \begin{equation} Z(\mathbf{a}, \epsilon_1,\epsilon_2,\Lambda) := \sum_{n = 0}^\infty \Lambda^n\...
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79 views

Finding the Hilbert expansion of a D4 Coulomb branch

I am trying to compute the HS of the following Coulomb branch, but first I am not sure how to proceed in interpreting the diagram and what variables to use. I am trying to use the equation from this ...
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180 views

Is a non-abelian gauge field's strength observable?

For an abelian gauge field, the field strength $G_{\mu \nu}$ is gauge-invariant. This means it is a physically observable quantity, e.g. we can build an apparatus to measure electromagnetic field ...
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129 views

Is there an algorithm to diagonalize a matrix using gauge transformations

I have two matrices $U(\lambda, x,t)$ and $V(\lambda, x,t)$, where $\lambda$ is a parameter, which belong to the $sl(2)$ algebra, and satisfy the zero-curvature equation $$ \partial_t U - \partial_x V ...
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212 views

AdS/CFT-duality: How does the $U(1)$ decouple form the $U(N)$?

A stack of N coincident D3-branes on its world-volume describe, at the lowest order in $\alpha'$ and in absence of non-trivial background fields, a supersymmetric $U(N)$ gauge theory as explained in ...
5
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552 views

Chern-Simons on a lattice and the framing anomaly

Can someone make or refer me to the argument for why $U(1)$ Chern-Simons theory in three dimensions cannot be defined by a lattice action? (Unlike Dijkgraaf-Witten theories, which are defined on the ...
5
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658 views

Getting Slavnov-Taylor identity

Let's have generating functional in path integral form for gauge $SU(n)$ theory with interaction: $$ \tag 1 Z[J] = \int DB D\bar{\Psi}D\Psi D\bar{c}Dc e^{iS}. $$ Here $$ S = S_{YM}(B, \partial B) + S_{...
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343 views

Naive questions on the classical equations of motion from the Chern-Simons Lagrangian

Consider a Chern-Simons Lagrangian $\mathscr{L}=\mathbf{e}^2-b^2+g\epsilon^{\mu \nu \lambda} a_\mu\partial _\nu a_\lambda$ in 2+1 dimensions, where the 'electromagnetic' fields are $e_i=\partial _0a_i-...
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842 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
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265 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields $F$ and $D$ which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
4
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Has the conjecture of Guillemin-Sternberg been proven for relevant physics cases?

From a working physicist's perspective, the conjecture of Guillemin-Sternberg (and its generalisations) seems to state in a highly technical manner that quantization commutes with gauge-fixing. In ...
4
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2answers
101 views

Gauge fixing, invertibility and Green's functional

consider the photon in QED and the corresponding EOM of its Green's functional in k-space: $$(k^\mu k^\nu-k^2g^{\mu\nu})\Delta_{\nu\rho}(k)=i\delta^\mu_\rho.$$ Now, I understand that $U^{\mu\nu}(k):=...
4
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1answer
87 views

Connection between gauge invariance and Lorentz invariance

This question is presented in the context of Weinberg's QFT book treatment, in particular considering the electromagnetism chapter. It begins in chapter 5 where Weinberg argues that in order to have ...
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If the gauge symmetry is not broken by spontaneous symmetry breaking, what symmetry is broken?

In this post, the answer by buzhidao showed that the $U(1)$ gauge symmetry is not broken by spontanous symmetry broken and Higgs mechanism. What role does "spontaneously symmetry breaking" ...
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45 views

Reference on instantons in gauge theories

Is there a reasonably detailed and systematic exposition of the theory of instantons in non-abelian gauge theories?
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45 views

Do longitudinal and scalar have anything to do with Faddeev-Popov ghosts?

In his this book, Hatfield calls ghosts the negative states appearing in the covariant (Gupta-Bleuler) quantization prescription of the electromagnetic field (page 89). When discussing Yang-Mills ...
4
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87 views

Which of the Wightman axioms are not incorporated by four dimensional quantum Yang-Mills?

I am trying to understand the quantum Yang-Mills existence problem but the best I have seen so far is the statement that there is no known interacting relativist field theory in four dimensions which ...
4
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0answers
71 views

Massless states on a compact manifold

I would like to understand the following statement found on page 6 second paragraph of 0305098. The authors discuss the quantization of the level $k$ of the WZW model for compact (and non-compact) ...
4
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136 views

Motivation for Non-Abelian Gauge Invariance

I have a very similar question to the one asked below: Why are non-Abelian gauge theories Lorentz invariant quantum mechanically? In particular, the setup to my question is essentially the same: ...
4
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0answers
255 views

How can I identify gauge transformations of fields with gauge transformations on a principal bundle?

I have some trouble with identifying what we do in physics regarding fields and bundle theory. I start from the following construction which I hope is ok: with a Lie group G and a smooth manifold M I ...
4
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0answers
101 views

Why is Lorenz gauge $\partial_\mu A^\mu = 0$ not attainable for 'permissible boundary conditions'?

I'm reading Paul Townsend's string theory lecture notes and I'm confused about a paragraph. Below, the $\varphi_i$ are first class constraints and the $\chi_i$ are gauge fixing conditions. ...
4
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133 views

On Seiberg-Witten curves

In page 44 of Gaiotto's article "Families of $\mathcal{N}=2$ Field Theories" on Teschner's review the author writes down the pure Seiberg-Witten curve as $$ x^2 = z^3 + 2uz + \Lambda^4z $$ with the SW ...
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146 views

Where does chiral matter at conical singularities “come from” in M-theory?

It seems to be accepted that to produce chiral fermionic matter in a compactification $\mathbb{R}^4\times X$ of M-theory/11d SUGRA to four dimensions, we need the seven-manifold $X$ to have isolated (...