Use this tag for topological field theory (Tft) and topological string theory (tst) questions.

learn more… | top users | synonyms (3)

3
votes
0answers
28 views

On open Gromov-Witten invariants of the projective line

apologies in advance in case this is a stupid question. I'm a mathematician interested in mathematical physics, but, again, penetrating the physics literature is not so easy for me. In the ...
1
vote
0answers
12 views

Correlation length during phase transitions in early Universe

During phase transitions of the second kind topological defects may form on the bounds of two areas separated by correlation length. In early Universe during phase transitions correlation length ...
1
vote
0answers
36 views

Representation theory and the Nekrasov partition function

Is there any review or lecture notes on the Nekrasov partition function which particularly thinks of this from a representation theorist's point of view? Some possibly related references I know of ...
0
votes
0answers
28 views

Topological configurations and phase transitions

It is known that topological defects might appear only during phase transitions of the first kind, while continuous transitions of the second kind and crossovers don't product them. How to explain ...
0
votes
0answers
43 views

Axion domain walls and QCD phase transition

Now it is known that QCD phase transition corresponds to crossover. This it seems that no topological defects is produced during phase transition. Do axion domain walls arise during QCD phase ...
0
votes
0answers
43 views

The bounds of axion domain walls are axion strings?

There are two phase transitions which are important for the axion physics. The first one is Peccei-Quinn phase transition, during which axions arise. The second one is QCD phase transition, at which ...
2
votes
1answer
47 views

Kalb-Ramond action and topological string radiation

Let's have simple scalar $\Phi$ action involves spontaneously symmetry breaking in a form $$ \tag 1 S = \int d^{4}x\left( |\partial_{\mu}\psi|^{2} + \psi^{2}|\partial_{\mu}\theta |^{2} - ...
1
vote
0answers
32 views

Global cosmic strings evolution

Recently I've read about axion string. It can be shown that the energy per unit length of the string located along $z$ axis is $$ \mu = 2 \pi f_{a}^{2}\ln\left( \frac{L}{\delta}\right), $$ where $L$ ...
2
votes
0answers
77 views

Axion strings and spontaneously broken symmetry

I have two question about axion strings: Why their appearance is connected with spontaneously broken symmetry? How to demonstrate that? Why they are stable topological configurations (look to the ...
2
votes
0answers
64 views

Choice of framing in Gravitational Chern-Simons

I was trying to understand formula(2.21) in Witten's paper "Quantum Field Theory and Jones Polynomial"(link: https://projecteuclid.org/euclid.cmp/1104178138) (Page 360). There, it was mentioned, the ...
2
votes
1answer
67 views

Fermion version of Gauss-Milgram sum?

For Bosonic topological order, a very useful formula was proved to be true: $\sum_a d_a^2 \theta_a=\mathcal{D} \exp(\frac{c_-}{8}2\pi i) $ (for more detail: $d_a$ is the quantum dimension of anyon ...
2
votes
2answers
61 views

Topological strings: Why is the complex structure for $T^2$ denoted as $\tau$ in string theory?

In these notes by Vafa on topological string theory he says in page 7 that the moduli of the 2-torus can be repackaged into two quantities: $$A=iR_1/R_2 \,\,\,\,\,\,\,\,\, \tau=iR_2/R_1$$ where $A$ ...
1
vote
1answer
101 views

What does it mean physically if pentagon identity or hexagon identity doesn't have any answers?

Imagine I write a fusion rule for some anyons on a paper. Then I try to solve pentagon identity and hexagon identity, imagine finally I find out for example Hexagonal equation doesn't have any ...
2
votes
2answers
215 views

Real World application of Topological Quantum Field Theory

What is a "killer-app" for the formalism of topological quantum field theory in "established real world physics"? To be more precise, I'm looking for an actual physical experiment, state of matter or ...
3
votes
0answers
71 views

A question about genus one string amplitude

In BCOV's paper http://arxiv.org/abs/hep-th/9309140 the genus one string amplitude of a Calabi-Yau 3-fold was explained in the B-model as the Ray-Singer torsion (there is a similar discussion in the ...
0
votes
1answer
75 views

Dilemma: Fusion space from a direct sum of anyons or NOT

In Preskill's note, 9.1.2 in page 44, concerning the fusion space, it states that: The fusion rules of the model specify the possible values of the total charge $c$ when the constituents have ...
0
votes
0answers
51 views

Topological term under electron-electron interaction

By integrating out fermions in gapped Dirac Hamiltonian, one can obtain a topological term for topological insulator. Why there is no further correction to this term when electron-electron interaction ...
3
votes
1answer
102 views

How the Vortex containing majorana bound state is non-abelian statistics

Recently,I read some papers about non-abelian statistics of majorana fermion, such as: Majorana Returns F. Wilczek http://www.nature.com/nphys/journal/v5/n9/full/nphys1380.html and Non-Abelian ...
1
vote
0answers
119 views

Topological theta term as a topological quantum field theory?

It is well known that the theta term $\int d^4x\frac{\theta}{4\pi}Tr[F\wedge F]=\int d^4x\frac{\theta}{4\pi}\epsilon_{\mu\nu\sigma\lambda}Tr[F^{\mu\nu}F^{\sigma\lambda}]$ is a topological term, ...
2
votes
1answer
40 views

transformations between 1st and 2nd order formalism in pure gravity

I am currently studying about 1st order formalism and I was wandering if the gauge transformation in the vielbein can be mapped to the coordinate transformation of the metric ( pure 2+1 gravity), ...
2
votes
2answers
174 views

Chern Simons action in 4 dimensions

I can not understand why we do not have a Chern-Cimons action for 4 or even forms? And why it not good theory for (3+1) dim?
5
votes
0answers
88 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 ...
0
votes
1answer
71 views

Reference request for supersymmetric localization

I would like to ask for some readable introduction or maybe review of the technique of supersymmetric localization for $\mathcal{N}=1,2$ SUSY theories. I would like a different one than the one people ...
4
votes
1answer
194 views

braiding bosons or fermions around majorana fermion

Majorana fermions are described by their topological charge. My question is whether we can see the topological charge of Majorana fermions by braiding a boson or a fermion around it ? Is the only ...
2
votes
0answers
158 views

Equations of motion in Maxwell-Chern-Simons theory [closed]

I've started with the Maxwell-Chern-Simons lagrangian (in 2+1 dimensions): $$L_{MCS}=-\frac{1}{4}F^{\mu \nu}F_{\mu\nu}+\frac{g}{2} \epsilon^{\mu \nu \rho}A_\mu\partial_\nu A_\rho$$ From this ...
0
votes
1answer
103 views

difference between classical vacuum solutions and instantons

What does the classical vacuum of the $SU(2)$ Yang-Mills action correspond to? Does it correspond to $F_{\mu\nu}=0$ everywhere or just at the spatial infinity? In Srednicki’s book, he has shown that, ...
2
votes
1answer
240 views

difference between instantons and sphalerons

What is the difference between instantons and sphalerons? If they are different, how do they violate baryon and lepton number in the standard electroweak theory?
2
votes
0answers
60 views

Weaker Formulations of Bulk-boundary Correspondence for Interacting Systems

From this post, it seems that bulk-boundary correspondence does not hold in general for interacting systems. What is meant by bulk-boundary correspondence there appears to be the existence of robust ...
1
vote
0answers
51 views

Topological S-matrix as an operator in the graphical calculus

My question comes from the following classic paper by Kitaev: Anyons in an exactly solved model and beyond (arXiv link) In Appendix E (pg 86), Kitaev introduces a diagram operator $S_z$ which acts ...
5
votes
4answers
269 views

Is gravitational Chern-Simons action “topological” or not?

Here are the 2+1D gravitational Chern-Simons action of the connection $\Gamma$ or spin-connection: $$ S=\int\Gamma\wedge\mathrm{d}\Gamma + \frac{2}{3}\Gamma\wedge\Gamma\wedge\Gamma \tag{a} $$ $$ ...
0
votes
0answers
42 views

Is there an analytical expression for the conductivity of the surface of topological insulators?

I have a question about the conductivity on the surface of Topological Insulators (TI): Is it accurate to model the conductivity by the Drude model (I read a paper that modeled the conductivity with ...
5
votes
1answer
317 views

“Topological” notions in physics

I've been trying to make sense recently of the usage of 'topological' in various fields of physics, and get sort of an intuition for what this means in context. This all boils down to my main question ...
3
votes
1answer
112 views

How to see the ground state degeneracy (GSD) from a $BF$ theory in $2+1$ $d$?

I have seen many times the $BF$ theory has non-trivial ground state degeneracy (typically on torus), but I can not see how the conclusion come out. Recently I found a paper by Hansson, Oganesyan and ...
3
votes
2answers
125 views

Relation between conformal and topological field theories

The Chern-Simons (CS) theory is a topological quantum field theory (TQFT). The question is, is a conformal field theory (CFT) a topological quantum theory? Or the reverse, topological quantum field ...
0
votes
0answers
41 views

Bound states and extensive field configurations

What are extensive field configurations in QFT (instantons, monopoles etc.)? What is the difference in description of their contribution in path integral value or in $n$-point operator functions ...
7
votes
0answers
323 views

TQFTs and Feynman motives

Questions Is a topological quantum field theory metrizable? or else a tqft coming from a subfactor? For a given metric, are there always renormalization and Feynman diagrams? Is there always a Feynman ...
2
votes
0answers
77 views

What is the definition of topological when talking about topological phases of matter?

What is the definition of topological when talking about topological phases of matter? Why do people think that the fractional quantum hall effect is topological? I think it means that the ground ...
6
votes
2answers
704 views

Definition of short range entanglement

When studying Symmetry Protected Topological phases, one needs to define what a short range entangled (SRE) states means. But there appears to be different definitions that are not equivalent to each ...
5
votes
1answer
124 views

No local degrees of freedom when connection is flat

I was studying Chern-Simons theory and variation of action gives us the flatness conditions $\mathrm{d} A + A \wedge A = 0$. I am wondering how to see that this implies there are no local degrees of ...
4
votes
0answers
184 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 ...
12
votes
0answers
349 views

Positivity for the level of Chern-Simons theory

In many classical papers about Chern-Simons theory (see, e.g. [1]), it is claimed that the Chern-Simons theories with gauge group $G$ are classified by an element of $k\in H^4(BG,\mathbb Z)$, the ...
2
votes
0answers
88 views

Relation between p+ip wave Superconductor and Moore-Read State

I am quite interested in the understanding of the relation between p_ip wave superconductor(SC) and the Moore-Read(MR) state. They share many similar properties, for example, p+ip SC has majorana as ...
6
votes
0answers
101 views

target category of extended field theory

For a topological field theory to be a true “extension” of an Atiyah-Segal theory, the top two levels of its target (ie its $(n-1)^{\text{st}}$ loop space) must look like $\text{Vect}$. What other ...
3
votes
0answers
87 views

Question about bosonization method

I have a question about bosonization method used in 1D system. Generally the bosonized field is assume to the following form \begin{equation} \psi = e^{i\phi}, \quad \phi = \phi^\dagger ...
6
votes
1answer
206 views

The 6-j symbol and intersecting Wilson loops, redux

This is a quite specific question continuing the problems I have with computing the expectation value of intersecting Wilson loops I laid out here. Using the tools from the answer there, I quite ...
8
votes
1answer
229 views

geometric quantization of the moduli space of abelian Chern-Simons theory

I wish to understand the statement in this paper more precisely: (1). Any 3d Topological quantum field theories(TQFT) associates an inner-product vector space $H_{\Sigma}$ to a Riemann surface ...
7
votes
1answer
352 views

Intersecting Wilson loops in 2D Yang-Mills

I am currently trying to understand 2D Yang-Mills theory, and I cannot seem to find an explanation for calculation of the expectation value of intersecting Wilson loops. In his On Quantum Gauge ...
1
vote
1answer
79 views

Interchaging boson and fermion on an infinite 1 dimensional line

In 1+1 dim bosonization, one introduce the Klein factors, which are Hermitian and satisfies Clifford algebra. (1) In the case of 1 dim space is a 1D ring ($S^1$ circle), then one have left-right ...
3
votes
1answer
178 views

Instanton in sine-Gordon equation

This is a statement from Giamarchi's book on Quantum Physics in 1D: "For a single-particle in a cosine potential, the slightest amount of tunneling between two cosine minima leads to conduction ...
3
votes
0answers
137 views

Proof for the Mass gap of sine-Gordon action with $g \cos(\beta \Phi)$

This is the sine-Gordon action: $$ \frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi + g \cos(\beta_{}^{} \cdot\Phi_{}) $$ ...