All Questions
Tagged with quantum-anomalies representation-theory
12
questions
0
votes
1
answer
85
views
Why is $Tr_R(T_a\{T_bT_c\})=-Tr_\overline{R}(T_a\{T_bT_c\})$ for $SU(N)$ representations?
I'm looking at the chiral anomaly in QFT and the term
$$d_{abc}=Tr_R(T_a\{T_b,T_c\})$$
shows up where $Tr_R$ means the trace in the representation $R$, $\overline{R}$ is the conjugate representation ...
- 248
1
vote
0
answers
153
views
Anomalies, 2-cocycles and (D+1)-cocycles
I'm learning about anomalies and I'm a bit confused about their relationships to 2-cocycles and 3-cocycles (in the group cohomology $H^{\bullet}(G, U(1))$). The below might only apply to 't Hooft ...
- 143
3
votes
1
answer
156
views
Apparent elimination of a 't Hooft anomaly in quantum spin system
The simplest system with a 't Hooft anomaly is the spin $\frac{1}{2}$ system with hamiltonian $\hat{H}=0$. The 't Hooft anomaly follows from the fact that such system has a trivial $SO(3)$ symmetry, ...
- 451
7
votes
1
answer
304
views
Why should a projective representation of a classical symmetry lift to a non-projective representation?
Background
Take a classical system with symmetry $G$. Suppose we can quantize this to a quantum system with Hilbert space $\mathcal{H}$. The state space of the quantum system is given by the ...
- 559
8
votes
1
answer
459
views
How projective representations can lead to 't Hooft anomalies in quantum mechanics?
In Shao's talk https://youtu.be/2vTvHYYl1Qk?t=1554, he argues that in quantum mechanics "if a symmetry acts projectively on states, then we have a t' Hooft anomaly". But I'm having trouble ...
- 451
9
votes
1
answer
369
views
Why are gauge anomalies characterised by the non-triviality of $\pi_5(\mathcal G)$?
The folklore in 4-dimensional gauge theories is that the existence of potential gauge anomalies from the triangle diagrams that need to be cancelled are characterised by the non-triviality of the ...
- 8,492
4
votes
1
answer
302
views
2D anomaly-free condition for a gauge theory
Take a $SU(2)$ gauge theory in 2d spacetime, say there are $n_1$ left-handed Weyl fermion in spin-1 written as
$$
1_L,
$$
and $n_0$ left-handed Weyl fermion in spin-0 written as
$$
0_L .
$$
and $n_{1/...
- 4,336
2
votes
1
answer
263
views
axial anomaly for adjoint fermion v.s. fundamental fermion
It is known that the axial anomaly (chiral anomaly, the left L- right R) shows that $U(1)_A$-axial symmetry is not a global symmetry at quantum level.
In particular, one can consider the (1) ...
- 4,336
5
votes
3
answers
1k
views
Anomaly of the $\text{U}(1)$-$\text{SU}(2)$-$\text{SU}(3)$ triangle diagram
In Srednicki's textbook "Quantum Field Theory", Problem 89.3 asks us to show that the Standard Model is anomaly free. I am puzzled by the triangle-vertex diagram whose external lines are a combination ...
- 1,653
7
votes
1
answer
624
views
Why is 2 a pseudoreal representation and there is no 2-2-2 anomaly?
In Srednicki's textbook "Quantum Field Theory", Problem 89.3 asks us to show that the Standard Model is anomaly free. The answer is given in the solutions manual. On page 150 of the solutions manual, ...
- 1,653
5
votes
1
answer
4k
views
Anomaly cancellation in the standard model (calculating the symmetrized trace of generators)
The Problem
We can show that the condition for the Standard Model to be anomaly-free is that the symmetrized trace over the generators of the gauge group vanishes:
\begin{align}
\text{tr} \big(\{\...
- 251
4
votes
2
answers
1k
views
Traces in different representation
I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental ...
- 662