Questions tagged [topological-field-theory]
Use this tag for topological field theory (Tft) and topological string theory (tst) questions.
431
questions
1
vote
2answers
37 views
Chern-Simon level quantization and quantum Hall effect
It is well-known that integer and fractional quantum Hall effect can be effectively described by $U(1)$ abelian Chern-Simon theory. In both cases, quantization(fractionalization) of Hall resistance is ...
0
votes
0answers
37 views
Topological Field Theory for Physicists [duplicate]
I was wondering if anyone knows good resources for Topological Field Theories aimed at physicists. In particular, I am looking for references which are full of examples, starting with simple toy ...
0
votes
1answer
33 views
What is the difference between topological theta term and Wess-Zumino-Witten term?
It seems that they both proportional to some thing like $\vec{n}\cdot \partial_{\tau}\vec{n}\, \times\,\partial_{s}\vec{n}$.
References: Fradkin, Quantum field theory: an integrated approach
0
votes
0answers
23 views
Regarding a possible duality between (2+1)D gravity and Chern-Simons Theory
Is there a duality between (2+1)D gravity and Chern-Simons Theory? Or they merely have related features? If so, of which type and why?
Thanks!
0
votes
1answer
32 views
Visualizing topological deformation and quantum mechanical interference
In section VI.1 of Zee's QFT, he says that for indistinguishable hard core particles in 2D, when comparing trajectories with different winding numbers:
Since the classes cannot be deformed into each ...
3
votes
0answers
50 views
Excitations of the string-net Hamiltonian
A quite general 2D topological order can be constructed through the string-net theory. Here, if the input data is some braided fusion category $C$ (i.e. the $F$-symbols), the elementary excitations ...
0
votes
0answers
26 views
What symmetry breaks in exciton condensation?
Recently the possibility of exciton condensates have shown up in some lattice TQFT models we've been studying, and I've been trying to learn more about them.
Suppose that we have a band insulator with ...
1
vote
1answer
51 views
What is the role of the dilaton in Jackiw-Teitelboim 2D gravity?
I read that the Einstein Hilbert action is topological in 2 dimensions. (What does that mean?). To write down a non-trivial action one introduces the dilaton field in JT gravity. Does this field have ...
5
votes
0answers
49 views
Physics behind the Kobayashi-Hitchin correspondence
Let $X$ be a $d$-dimensional Kähler manifold with Kähler matric $\omega$. Let's consider the following setups:
Suppose $E \rightarrow X$ is hermitian vector bundle with hermitian connection $A$. In ...
1
vote
1answer
32 views
Classification of topolgical phases when eigenstates belong to complex Grassmannian
I want to understand the paper which belongs to Ludwig (I put it below). I do not understand why exactly he got the new space $U(m+n)/U(m) \times U(n)$. My understanding from Grassmannian Manifold is ...
1
vote
0answers
36 views
Physical origin of coisotropic branes
The paper "Remarks on A-branes, Mirror Symmetry, and the Fukaya category" develops the possibility of A-model open strings ending on a coisotropic submanifold equipped with a holomorphic ...
3
votes
0answers
54 views
Mass deformations in D-brane systems
It is well known that the worldvolume theory of $N$ coincident D$p$-branes is given by the $U(N)$ Yang-Mills theory in $(p+1)$-dimensions. One important feature of this setup is the possibility of ...
0
votes
0answers
21 views
Rigorous definition of “condensation” in Topological Lattice Gauge theories?
I have encountered the term "string-net condensation" in the string-net paper by Levin-Wen, and in Kitaev's Toric Code - where we say that the ground state is a string net condensate and (I ...
3
votes
1answer
123 views
Deriving the Topological Descent Equations
I am trying to show that in a cohomological TQFT, given a physical operator $\phi^{(0)}$, one can construct a chain of non-local physical operators. In doing so, I need to show that a certain set of ...
10
votes
2answers
153 views
How to calculate a TQFT Gaussian path integral from Seiberg's “fun with free field theory”?
In his talk "Fun with Free Field Theory", Seiberg discusses a topological quantum field theory in $d+1$ dimensions with the action
$$ S = \frac{n}{2\pi} \int \phi\, \mathrm{d} a \tag{1}$$
...
0
votes
0answers
22 views
S-Matrix of Modular Tensor Category and physical S-matrix
Let $\mathscr{C}$ be a Modular Tensor Category (MTC). Then it has a finite set of simple objects $\{X_i\}$. Moreover, we define the S-matrix as $$S_{ij} = \text{Tr}(B_{X_i,X_j}^{-1}B_{X_j,X_i})$$
...
3
votes
1answer
46 views
A pedagogical semi-rigorous review of topological phases, topological order, and related subjects
I'm looking for a pedagogical review or book about topological phases, topological order, TQFTs, and related subjects.
The ideal thing would be a mix of rigorous definitions and physical examples, ...
3
votes
1answer
91 views
Why is Kitaev's toric code a $Z_2$ gauge theory?
I am reading Kitaev's 2003 paper. In the literature, it is often said that the model proposed in this paper is a $Z_2$ gauge theory. I don't quite see why it is the case. Where is the $Z_2$ gauge ...
0
votes
0answers
22 views
Topological defects in general and Chern-Simons in particular
I'm trying to gain intuition on some physical concepts that I cannot yet fully understand, and I think many of you can help me.
Is it correct to think of of a topological defect as the addition ad hoc ...
12
votes
3answers
1k views
What is the physical importance of topological quantum field theory?
Apart from the fascinating mathematics of TQFTs, is there any reason that can convince a theoretical physicist to invest time and energy in it?
What are/would be the implications of TQFTs?
I mean is ...
1
vote
1answer
125 views
Why do we call fracton by its name?
I am reading on fractons. In the literature, it is said that factons are fractionalized excitations.
My understanding about fractons is that it is energetically costly to move fractons, and in this ...
2
votes
0answers
19 views
Partition functions of descendent SPTs of the Haldane chain
The Haldane chain can be viewed as a $1+1$ D SPT protected by an $SO(3)$ symmetry. If this SPT is put on a triangulated closed manifold $X$, its partition function can be written as
$$
e^{i\pi\...
5
votes
1answer
192 views
Criteria to Define a (Classical) Topological Field Lagrangian? + Conjecture
I have a question concerning topological field theories. I'd rather keep the discussion at the classical level, so as to concentrate on the feature of topological evolution, which is what interests me ...
4
votes
1answer
138 views
The argument for a mass gap for the $O(3)$ Heisenberg ferromagnet
One possible argument for asymptotic freedom in the 2D $O(3)$ ferromagnetic Heisenberg model is the existence of so-called instantons, discovered in the 1975 paper of Belavin and Polyakov. This is ...
2
votes
0answers
68 views
Excitations & Pentagon axiom in algebraic theory for anyons
I have been reading the anyon theory by Kitaev and Wang. I have two possibly related questions:
Why is the Pentagon equation/axiom sufficient for characterizing associative relations?
Are there anyon ...
1
vote
1answer
42 views
Magnetization and Polarization in an electromagnetic field theory
I am currently reading through a paper by Hughes and Ramamurthy (ref: https://arxiv.org/abs/1508.01205), which describes the electromagnetic response of a line-node semimetal by the action
$$S[A,B] = \...
4
votes
1answer
105 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
72 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
85 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
251 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:
$$Tr(-1)^FF_LF_Rq^{...
11
votes
2answers
338 views
Is it possible to bound a single D0-brane to a D4-brane?
I'm studying the Jafferis solution for twisted $N=4$ Yang-Mills theory in four dimensions from the paper Crystals and intersecting branes.
Consider the problem of computing the charges of the allowed ...
5
votes
1answer
150 views
Holomorphic anomaly at genus 1
Partition function on torus can be defined using a generalized Witten like index as given below:
$$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}},$$
where $\...
3
votes
1answer
182 views
References on mathematical stacks for a string theory student
This question was posted on mathoverflow (here) without too much success.
I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" ...
1
vote
0answers
46 views
Why string amplitude could be computed by path integral of string field theory?
I am trying to understand BCOV's paper: Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes.
In this paper, it was shown that the higher genus string amplitude for B-...
5
votes
3answers
202 views
How is cohomology theory used in quantum field theory?
Quantum field theory uses a large amount of mathematics and I was wondering about some applications of cohomology theory in QFT, I understand it has applications in string theory but I was wondering ...
1
vote
0answers
47 views
Staggered Zeeman field in topological magnetic insulators
I was reading the following paper. However, I do not understand a crucial part of their argumentation. They add a parity (P) and time (T) symmetry breaking term to the Hamiltonian in eq (2). Then they ...
3
votes
0answers
50 views
Topological Descent Equation
Assume that we have a cohomological field theory, with an odd symmetry generated by an odd operator $Q$ and an exact energy momentum tensor $T_{\mu\nu}=[Q,G_{\mu\nu}]$. Then by integrating over an ...
1
vote
1answer
55 views
One question about topological excitation in quantum many body system
I attended a lecture given by Professor Wen Xiaogang.
In the lecture, Prof.Wen gave an example of topological excitation:
For a state $$(\uparrow\downarrow)(\uparrow\downarrow)(\uparrow\downarrow)(\...
2
votes
0answers
17 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
70 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
1answer
111 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
83 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
$$
Z(\lambda)=\sum_{i=1}^n\lambda_i^{g-...
asked Sep 7 '20 at 22:17
AccidentalFourierTransform
42.3k20 gold badges93 silver badges187 bronze badges
6
votes
0answers
84 views
Are Chern-Simons theories classified by bordism groups?
For a long time it was thought that anomalies for a group $G$ were classified by $H^n(BG)$, although it is now understood that they are in fact classified by $\Omega^n(BG)$.
On the other hand, ...
asked Sep 5 '20 at 15:27
AccidentalFourierTransform
42.3k20 gold badges93 silver badges187 bronze badges
0
votes
1answer
67 views
Topology in quantum materials
So far I have learned about topological quantum material, my understanding is that topological order in a quantum material is the way the eigenvectors of the Hamiltonian of the system aligned. So if I ...
2
votes
0answers
44 views
References for topological strings on supermanifolds
This question concerns topological string theory.
It was known sice its outset, that the BRST-cohomology ("the ring of observables") of the weakly coupled B-model topological string on a ...
8
votes
0answers
80 views
2. Topological field theories in two-dimensions$.$
It is known that 3d TQFTs are classified by modular tensor categories, and 2d TQFTs by Frobenius algebras.
A 3d TQFT on a manifold of the form $S^1\times M_2$ induces a 2d TQFT on $M_2$. So there must ...
asked Aug 28 '20 at 17:56
AccidentalFourierTransform
42.3k20 gold badges93 silver badges187 bronze badges
2
votes
0answers
41 views
Deducing fusion rules of non-abelian fluxons
I have been reading about non-abelian fluxons in John Preskill's lectures notes on topological quantum computing and I do not understand how he deduced the fusion rules for fluxons in the example he ...
8
votes
2answers
384 views
1. Topological field theories in two-dimensions$.$
The paper arXiv:hep-th/9308043 proves that the partition function of an arbitrary (unitary) two-dimensional topological theory is given by
$$
Z(\lambda)=\sum_{i=1}^n\lambda_i^{g-1}\tag1
$$
where $g$ ...
asked Aug 22 '20 at 17:47
AccidentalFourierTransform
42.3k20 gold badges93 silver badges187 bronze badges
1
vote
0answers
74 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 ...
