All Questions
23
questions
2
votes
1
answer
143
views
Spontaneous Symmetry Breaking, Vacuum Degeneracy, and Goldstone Bosons applied to large gauge transformations
I am reading Strominger's lecture notes on the infrared structure of gravity and gauge theory. I am trying to understand subchapter 2.11, where the author focuses on the notions of "Spontaneous ...
- 3,992
3
votes
0
answers
180
views
Witten anomaly and bound states of fermions
In his famous paper "An SU(2) anomaly", Witten begins by noting that an SU(2) gauge theory with a single fermion in the doublet representation is weird, since there is "no obvious ...
1
vote
0
answers
210
views
Question on the Background Field Method for Non-Abelian Gauge theory
I am reading Peskin's and Schroeder's book "An Introduction to Quantum Field Theory". In Chapter 16.6 the authors use the Background Field Method to determine the $\beta$ function for a non-...
- 3,992
7
votes
0
answers
212
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 ...
6
votes
1
answer
206
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, ...
7
votes
0
answers
108
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
$$
\...
3
votes
0
answers
80
views
What is the topological data for $(\mathbb Z_n)_p$ theories?
Consider the 3d TQFT described by the Lagrangian (Dijkgraaf-Witten with gauge group $\mathbb Z_n$ at level $p$):
$$
\mathcal L=\frac{n}{2\pi} B\wedge\mathrm dA+\frac{p}{4\pi}A\wedge\mathrm dA
$$
with $...
6
votes
1
answer
358
views
Peculiarities of non-Abelian gauge groups: self-coupling and topology
There are two striking aspects of non-Abelian gauge groups (compared to their Abelian cousins):
(1) The pure gauge parts of non-Abelian Lagrangians contain self-interaction terms that are trilinear ...
- 1,783
4
votes
0
answers
183
views
Gauging a mixture of internal and spacetime symmetries
Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a space-...
- 66
2
votes
1
answer
341
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 ...
- 299
4
votes
1
answer
705
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 ...
- 7,848
14
votes
1
answer
817
views
Anomalies for not-on-site discrete gauge symmetries
If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
- 8,064
18
votes
2
answers
7k
views
The phrase "Trace Anomaly" seems to be used in two different ways. What's the relation between the two?
I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing.
The first way I've seen it used is in the manner, for ...
- 3,492
3
votes
1
answer
499
views
How to justify matter-field interaction for non-gauge-invariant Hamiltonian?
I'm wondering how can one formally justify the electromagnetic response of a system which does not verify local U(1) gauge invariance.
A good example of what I would like to consider is given by the ...
- 10.6k
2
votes
2
answers
569
views
Gauge invariant scalar potentials
If $\Phi$ is a multi-component scalar field which is transforming in some representation of a gauge group say $G$ then how general a proof can one give to argue that the potential can only be a ...
- 4,619