Questions tagged [topological-field-theory]
Use this tag for topological field theory (Tft) and topological string theory (tst) questions.
409
questions
0
votes
1answer
8 views
Magnetization and Polarization in an electromagnetic field theory
I am currently reading through a paper by Hughes and Ramamurthy (ref: https://arxiv.org/abs/1508.01205), which describes the electromagnetic response of a line-node semimetal by the action
$$S[A,B] = \...
4
votes
1answer
74 views
Why is $T^*S^3$ a conifold?
So, I was reading the famous Gopakumar Vafa paper, and they mention that $T^*S^3$ is a conifold. Why is this the case? I would naively expect $T^*S^3$ to be basically the same everywhere ($S^3$ is a ...
2
votes
0answers
42 views
lecture notes about the relation between algebraic topology, topological quantum field theory, condensed matter physics [closed]
I am an undergraduate student and I am very interested in topology with its application in physics. So last year I've read some books about this field, mainly about topological soliton, some ...
2
votes
1answer
72 views
A-brane boundary conditions
This question concerns the boundary conditions that A-branes solve.
Consider the following problem: Suppose that an A-brane wraps a submanifold $Y$ of $X$. Let $\mathcal{L} \rightarrow Y$ be a rank ...
6
votes
0answers
210 views
Holomorphic instantons in target torus
For computing instantons contributions from worldsheet torus to target torus, one can evaluate zero modes contribution of genus 1 partition function given by following expression:
$$Tr(-1)^FF_LF_Rq^{...
10
votes
1answer
286 views
Is it possible to bound a single $0$-brane to a $4$-brane?
I'm studying the Jafferis solution for twisted $N=4$ Yang-Mills theory in four dimensions from the paper Crystals and intersecting branes.
Consider the problem of computing the charges of the allowed ...
5
votes
1answer
138 views
Holomorphic anomaly at genus 1
Partition function on torus can be defined using a generalized Witten like index as given below:
$$F_1=\int_\mathbb{T}\frac{d^2\tau}{\tau_2} Tr(-1)^F F_LF_R \;q^{L_0} \bar{q}^{\bar{L_0}},$$
where $\...
3
votes
1answer
140 views
References on mathematical stacks for a string theory student
This question was posted on mathoverflow (here) without too much success.
I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" ...
1
vote
0answers
40 views
Why string amplitude could be computed by path integral of string field theory?
I am trying to understand BCOV's paper: Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes.
In this paper, it was shown that the higher genus string amplitude for B-...
5
votes
3answers
173 views
How is cohomology theory used in quantum field theory?
Quantum field theory uses a large amount of mathematics and I was wondering about some applications of cohomology theory in QFT, I understand it has applications in string theory but I was wondering ...
1
vote
0answers
42 views
Staggered Zeeman field in topological magnetic insulators
I was reading the following paper. However, I do not understand a crucial part of their argumentation. They add a parity (P) and time (T) symmetry breaking term to the Hamiltonian in eq (2). Then they ...
1
vote
0answers
32 views
Topological Descent Equation
Assume that we have a cohomological field theory, with an odd symmetry generated by an odd operator $Q$ and an exact energy momentum tensor $T_{\mu\nu}=[Q,G_{\mu\nu}]$. Then by integrating over an ...
1
vote
1answer
52 views
One question about topological excitation in quantum many body system
I attended a lecture given by Professor Wen Xiaogang.
In the lecture, Prof.Wen gave an example of topological excitation:
For a state $$(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\...
2
votes
0answers
16 views
Quantum Hall effects with an additional uniform unit flux on a compact manifold
I have two questions:
Let us imagine that we have an integer quantum Hall system with electric Hall conductance as $\sigma_\text{H}$ on a two-dimensional (spatial) torus with size $L_1\times L_2$. If ...
2
votes
0answers
63 views
Topological Quantum Field Theory with Symmetries and Knot Quandles
It is well known that Chern-Simons theory provides an intrinsically three dimensional way to compute knot invariants like the Jones Polynomial. 3D TQFTs also have an algebraic description in terms of ...
5
votes
0answers
81 views
D-branes as the atoms of Calabi-Yau crystals
I'm studying the Nishinaka-Yoshida crystal models that encode the generating function of $D4$-$D2$-$D0$ BPS bound states on a Calabi-Yau divisor.
The case of conifold at its singular point is ...
3
votes
1answer
72 views
3. Topological field theories in two-dimensions$.$
As in my previous two posts (1 & 2), a unitary two-dimensional TQFT is specified by a set of real numbers $\{\lambda_i\}$ such that the partition function is
$$
Z(\lambda)=\sum_{i=1}^n\lambda_i^{g-...
asked Sep 7 '20 at 22:17
AccidentalFourierTransform
39k15 gold badges89 silver badges174 bronze badges
6
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0answers
75 views
Are Chern-Simons theories classified by bordism groups?
For a long time it was thought that anomalies for a group $G$ were classified by $H^n(BG)$, although it is now understood that they are in fact classified by $\Omega^n(BG)$.
On the other hand, ...
asked Sep 5 '20 at 15:27
AccidentalFourierTransform
39k15 gold badges89 silver badges174 bronze badges
0
votes
1answer
60 views
Topology in quantum materials
So far I have learned about topological quantum material, my understanding is that topological order in a quantum material is the way the eigenvectors of the Hamiltonian of the system aligned. So if I ...
2
votes
0answers
40 views
References for topological strings on supermanifolds
This question concerns topological string theory.
It was known sice its outset, that the BRST-cohomology ("the ring of observables") of the weakly coupled B-model topological string on a ...
8
votes
0answers
74 views
2. Topological field theories in two-dimensions$.$
It is known that 3d TQFTs are classified by modular tensor categories, and 2d TQFTs by Frobenius algebras.
A 3d TQFT on a manifold of the form $S^1\times M_2$ induces a 2d TQFT on $M_2$. So there must ...
asked Aug 28 '20 at 17:56
AccidentalFourierTransform
39k15 gold badges89 silver badges174 bronze badges
2
votes
0answers
35 views
Deducing fusion rules of non-abelian fluxons
I have been reading about non-abelian fluxons in John Preskill's lectures notes on topological quantum computing and I do not understand how he deduced the fusion rules for fluxons in the example he ...
8
votes
2answers
356 views
1. Topological field theories in two-dimensions$.$
The paper arXiv:hep-th/9308043 proves that the partition function of an arbitrary (unitary) two-dimensional topological theory is given by
$$
Z(\lambda)=\sum_{i=1}^n\lambda_i^{g-1}\tag1
$$
where $g$ ...
asked Aug 22 '20 at 17:47
AccidentalFourierTransform
39k15 gold badges89 silver badges174 bronze badges
1
vote
0answers
71 views
Physical interpretation of TFTs
1. Defining TFTs
Let $n$ be a positive integer and $\mathbb k$ be a field.
In my lecture I was introduced to TFTs using the following definition going back to Atiyah (around 1988):
A $n$-dimensional, ...
1
vote
0answers
28 views
Why is short-range entanglement defined in terms of its possible deformations?
After reading the question and answers in Definition of short range entanglement I wonder why the definition of a short-range entangled state is given in terms of its possible deformations -
A SRE ...
1
vote
0answers
25 views
Two dimensional conformal field theories with changing central charge
For two-dimensional conformal field theories it is usually assumed that the cental charge is fixed (for simplicity let's assume that $c=\bar c$).
Is there a generalization or a concept that uses the ...
4
votes
1answer
124 views
Chern-Simons (CS) theory
I have a question about Constructuion of Chern-Simon Action.
In its paper "Non-commutative geometry and string field theory", Witten construct the Action of the String Field Theory inspiring ...
6
votes
0answers
62 views
$F$-symbols for compact Lie groups
Moore and Seiberg (1989) prove that rational CFTs are classified by the braiding matrices
$$
B\begin{bmatrix}j_1&j_2\\i&k
\end{bmatrix}\colon \bigoplus_p V_{j_1p}^i\otimes V_{j_2k}^p\to V_{...
2
votes
0answers
59 views
Expectation value of Wilson loop in Chern-Simons theory
I have read Witten's paper, and I am interested on computing the expectation value of a Wilson loop with a representation $R$ on Chern-Simons theory in $d=3$. I am especially interested in cases for $...
5
votes
0answers
68 views
Lost reference: Kähler gravity in six dimensions and three dimensional $SL(2,\mathbb{C})$ Chern-Simons theory
I've noticed that several references take for a fact that by studying Kähler gravity on a Calabi-Yau threefold one can demostrate that any lagrangian submanifold embedded in the threefold posees three ...
3
votes
1answer
60 views
Definition for long range entanglement (LRE) by generalized local unitary (gLU) and generalized stochastic local (gSL) transformations
I am studying this book: Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems (https://arxiv.org/abs/1508.02595).
In chapter 7, it introduces ...
3
votes
1answer
113 views
Winding number is an integer
In computing the variation of the action in Chern-Simons, and in other contexts, we get the following expression that is named the winding number, where $U$ comes from a gauge transformation:
$$ W[U] =...
2
votes
1answer
95 views
What is the Topologically Twisted Index?
I know that one can take a supersymmetric theory defined on $\mathbb{R}^n$ and topologically twist it by redefining the rotation group of the theory into a mixture of the (spacetime) rotation group ...
4
votes
1answer
136 views
What is a Topological Twist?
I have come across topological twists on numerous occasions but I have never actually seen them explained in an understandable way. So, I was wondering
What does it physically mean to topologically ...
4
votes
0answers
58 views
How does anomaly inflow work in terms of the eta invariant?
I'm trying to understand the non-perturbative picture of anomaly inflow, mainly following these two articles by Witten and Yonekura:
[1] - https://arxiv.org/pdf/1909.08775.pdf ,
[2] - https://arxiv....
3
votes
0answers
107 views
What is an NS-2 brane?
This question is about topological string theory and it was also posted in MathOverflow.
The existence of a new brane called "an NS-2 brane" is predicted in (the second paragraph in the page ...
5
votes
1answer
257 views
Integrating over non-trivial fiber bundles - Chern-Simons Theory
I have been reading Tong's notes on QHE and Gauge Theories, specifically the part about quantizing the Abelian U(1) Chern-Simons level at finite temperature in the presence of a monopole (These ...
7
votes
1answer
108 views
Can a symmetry of a topological field theory be spontaneously broken?
There are examples of topological "terms" causing spontaneous symmetry breaking. One that comes to mind is the $\theta$ term in $4d$ $SU(N)$ Yang-Mills, which at $\theta=\pi$ spontaneously breaks time ...
2
votes
0answers
39 views
Chiral anomaly in Weyl semimental
In Weyl semimetal, there is an analog of ABJ anomaly, which is a $E \cdot B$ term. The ABJ anomaly can be viewed as winding number because of the homotopy group of sphere $\pi_3(S^3)= \mathbb{Z}$ for ...
6
votes
1answer
216 views
On TQFT and theories without propagating degrees of freedom
Maybe not a very sensible question, but I would like to know, whether there exist topological field theories (TQFT) with propagating degrees of freedom, or, conversely, theories without propagating ...
0
votes
0answers
21 views
Can Berry phase been carried by bulk electrons in TIs?
I'm studying 3D topological insulators and more in particular, weak antilocalization (WAL) effects, so I know that they are characterized by a $\pi$ Berry phase that gives rise to destructive ...
0
votes
0answers
64 views
Question about the proof of different contractions for the effective Brillouin zone differing by an even Chern number
I am reading Moore and Balents'paper (DOI: 10.1103/PhysRevB.75.121306) which proves the Z2 invariant is the parity of the Chern number for the effective Brillouin zone. I am confused about some ...
5
votes
1answer
86 views
Difference between TCFTs and 2D TQFTs
I have been reading a lot lately on Topological String Theory and general TQFTs and as I noticed, in most contexts the terms "2-dimensional TQFT" and "Topological Conformal Field Theory" (TCFT) seem ...
2
votes
0answers
44 views
free fermion- monopole operator in scalar $QED_3+$ Chern simons term equivalence proof?
In most papers discussing 3D Abelian bosonization duality, they say that monopole operator in scalar $QED_3+CS$ is dual to free fermions.
How do they know it, because I have never seen an actual ...
4
votes
0answers
74 views
The value of Gravitational Chern Simons theory integration on some three manifolds
Consider the 3d gravitational Chern Simons theory
$$S= \frac{k}{192 \pi} \int_{M_3} \mathrm{Tr}\left(\omega\; \mathrm{d} \omega + \frac{2}{3}\omega^3\right)$$
where $\omega$ is the spin-connection on ...
1
vote
1answer
54 views
Chern-Simons term in Coulomb or radiation gauge
In some of the literature (for example, below Eq. (A3) of this paper), the following is claimed to be the Chern-Simons term in the Coulomb gauge:
\begin{equation}
2a_0(\partial_1a_2-\partial_2a_1)
\...
3
votes
0answers
85 views
Winding number of QCD vacuum
We know that QCD vacuum has instantons, which corresponds to tunneling process. Consider $SU(2)$ gauge theory without matter. We say that in the classical configuration of vacuum state $F^a_{\mu\nu}=0$...
2
votes
0answers
21 views
Mutual statistics between dyons (charge-monopole composite)
I am asking for some intuitive understanding between two dyons with $(e,m)$ in 3-dimensional space. Here the magnetic charge $m$ is normalized as
\begin{eqnarray}
m=\int_{S^2}\frac{B}{2\pi}\in\mathbb{...
3
votes
1answer
60 views
Why do not we consider the topological term in Abelian gauge theory?
The second Chern form $\epsilon^{\mu\nu\rho\sigma} F_{\mu\nu}F_{\rho\sigma}$ is topological in 4-dimensional spacetime. However, we usually only consider this term in non-Abelian gauge theory, but not ...
4
votes
1answer
82 views
Normalization of the Chern-Simons action in the Dijkgraaf-Witten paper
I am trying to understand the seminal paper "Topological gauge theories and group cohomology" by Dijkgraaf and Witten. They consider an oriented three-manifold $M$, compact Lie group $G$ and a $G$-...
