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.

462 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
65
votes
1answer
3k views

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 ...
55
votes
0answers
1k 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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
47
votes
0answers
2k 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 ...
11
votes
0answers
335 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 ...
11
votes
0answers
208 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)? ...
9
votes
0answers
347 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 ...
9
votes
0answers
1k 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.). ...
9
votes
0answers
279 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 ...
9
votes
0answers
187 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 ...
8
votes
0answers
204 views

't Hooft Anomaly Equivalent Definitions

I've seen a 't Hooft anomaly defined in two ways. Roughly, a theory has a 't Hooft anomaly when Once the theory is coupled to a background gauge field $A$ (so study eg the partition function $Z[A]$), ...
8
votes
2answers
237 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):=...
8
votes
1answer
251 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 ...
8
votes
0answers
291 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 $$...
8
votes
0answers
124 views

Axial and vector resonances in composite Higgs models

Is there a reason to believe that the axial resonances are heavier than the vector resonances in the composite Higgs models? For instance, in this article, to have zero tree level contributions to S ...
7
votes
0answers
69 views

Why is the group of gauge transformations on the frame bundle isomorphic to $\text{Diff}(M)$?

Consider the frame bundle $LM \to M$ for given Lorentzian manifold $M$. The group $\mathcal{G}$ of gauge transformations of the second kind are automorphisms $\phi:LM \to LM$ covering the identity $\...
7
votes
0answers
136 views

Where do theta terms live?

Consider a gauge theory with group $G$. The canonical kinetic term for the gauge field is $F\wedge\star F$ and, depending on the dimensionality of spacetime, there are other allowed terms, such as ...
7
votes
0answers
144 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 ...
7
votes
0answers
304 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 ...
7
votes
0answers
146 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
109 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
votes
0answers
111 views

Systematically constructing a Lagrangian with given Poincare representations for particles

In one approach to constructing field theories, we begin with some desired particle content (e.g. a massive spin-1 particle), and then we construct a corresponding classical Lagrangian (e.g. the Proca ...
6
votes
0answers
195 views

What is Noether's Second Theorem?

I have been unable to find a short statement of Noether's second theorem. It would be helpful to have the following: A short mathematical statement of the theorem. Does it imply a conservation law ...
6
votes
1answer
93 views

What causes here an apparent violation of Elitzur's theorem?

Elitzur's theorem [Ref. Andreas Wipf, Statistical approach to quantum field theory] states that A local gauge symmetry cannot break spontaneously. The expectation value of any gauge non-invariant ...
6
votes
0answers
202 views

A Naive Question about Gauge Theory

I am suffering from a question I encountered from the lecture notes of gauge theory by David Tong. The problem comes from page 67 on the gauge fixing in back-ground gauge method. In David Tong's ...
6
votes
0answers
238 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
votes
0answers
125 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. Whenever $\...
6
votes
0answers
537 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\...
6
votes
0answers
673 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 ...
6
votes
0answers
257 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
299 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 ...
6
votes
0answers
172 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 ...
6
votes
0answers
234 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
1answer
108 views

What is the analogy between the gauge covariant derivative and the covariant derivative in General Relativity?

A particle in the Dirac field can be described with the following equation $$i\gamma^\mu\partial_\mu\psi-m\psi=0$$ This is if the particle is non-interacting. However, if we impose a local $U(1)$ ...
5
votes
0answers
59 views

How do you write a resolution of unity (the identity) in gauge theories?

In, say, a quantum field theory of a single scalar field $\phi$, it is common to write the identity as ${\bf 1}=\int{\cal D}\phi\, |\phi\rangle\langle \phi|$, a useful thing to do in various path ...
5
votes
0answers
97 views

Solving equations of motion of holomorphic BF theory - pure gauge in complex coordinates

In this paper by Bailieu and Tanzini, aspects of holomorphic BF theory are presented. Holomorphic BF theory on a four dimensional Kahler manifold is discussed from page 5, and on page 8 the ...
5
votes
0answers
83 views

Stueckelberg mechanism in path integrals

Suppose we have some gauge invariant Lagrangian $\mathcal{L}_0$ depending on $A$ and some matter fields $\psi$, and we add a mass term for $A$. $$\mathcal{L}[A,\psi]=\mathcal{L}_0[A,\psi]+m^2A^2$$ ...
5
votes
0answers
72 views

Can you do gauge theories over topological groups?

Quantum gauge theories involve (functional) integration over a Lie group. Is there any meaningful generalisation to (non-manifold) topological groups? Consider for example the Whitehead tower $$ \...
5
votes
0answers
138 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 ...
5
votes
0answers
159 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 ...
5
votes
0answers
119 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 $U(1)$ ...
5
votes
0answers
178 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 (...
5
votes
0answers
85 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 ...
5
votes
0answers
365 views

Scalar photon states

I don't really understand what a scalar photon physically is. I know that in the Coulomb gauge the normal mode expansion of potential $A^{\mu}$ is given by the two transverse polarization, which ...
5
votes
0answers
236 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 ...
5
votes
0answers
174 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 ...
5
votes
0answers
243 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
votes
0answers
820 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_{...
5
votes
0answers
382 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-...
5
votes
0answers
134 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 ...
5
votes
1answer
1k 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 - ...

1
2 3 4 5
10