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

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2
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115 views

Holonomy twisting

There is Witten's topological twist of standard SUSY QFTs with enough SUSY into Witten-type TQFTs. What is a holonomy twist?
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1answer
91 views

Question about charge conservation at vertices of web diagram

My question is about web diagram in paper of Aganagic et al. How to get the $\alpha-\beta$ line rather than $-\alpha+\beta$ line of rightmost diagram of fig.3? More precisely, how to show the charge ...
7
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0answers
258 views

How does Haldane conjecture follow from the topological $\Theta$ term

The one dimensional SU(2) Heisenberg quantum spin chain is known to be described by the 1+1d O(3) nonlinear $\sigma$ model with a $\Theta$ term, following the action ...
5
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1answer
131 views

How to determine R charge?

Ref. 1, page 15, equation (23) defines the $U(1)_V$ and $U(1)_A$ actions as $$e^{i\alpha F_V}: \Phi(x,\theta^{\pm},\bar{\theta}^{\pm}) \rightarrow e^{i\alpha q_V}: \Phi(x,e^{-i\alpha ...
2
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3answers
93 views

Valid theory in all dimensions for solitary waves

I'm studying soliton (solitary waves). They are many theory which explain the phenomenon, like sine-Gordon model. But sine-Gordon model has limitations when it applies to 4 dimension because it is ...
5
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2answers
220 views

How to understand worldsheet fermion as a section?

I am reading Witten's paper on topological string, and I found some mathematical notation is hard to understand for me. Consider the nonlinear sigma model in 2 dimensions governed by maps $\Phi : ...
6
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1answer
100 views

About Vanishing of BRST commutator in path integral

In Witten's paper Topological Quantum Field Theory, about formula (3.2), the property $<\{Q,\mathcal{O}\}>=0$ depends on the assertion that $Z_{\varepsilon}(\mathcal{O})= \int \mathcal{D}X ...
7
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1answer
105 views

Do instantons support quantum bound states?

When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...
9
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2answers
384 views

Algebraic/Axiomatic QFT vs Topological QFT

Can anybody please tell me a good source investigating the relation between Algebraic/Axiomatic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT)? Or is there none?
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2answers
479 views

Gauge invariance and diffeomorphism invariance in Chern-Simons theory

I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to ...
7
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1answer
191 views

topological twisting by introducing bosonized operator

In this paper http://arxiv.org/abs/hep-th/9309140 on page 125, the authors claim that one can twist the $N=2$ theory by introducing a term in the action $\frac{1}{2}\int R \phi$, where $\phi$ is the ...
8
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3answers
333 views

Chern-Simons degrees of freedom

I'm currently reading the paper http://arxiv.org/abs/hep-th/9405171 by Banados. I am just getting acquainted with the details of Chern-Simons theory, and I'm hoping that someone can explain/elaborate ...
2
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1answer
168 views

A classically trivial quantum field theory of electromagnetism

Presumably there is a field theory of electromagnetism that classically gives trivial equations of motion, but when quantized shows interesting topological phenomena. I am talking about the Lagrangian ...
5
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0answers
187 views

Reference on Chern-Simons theory [duplicate]

I have recently been trying to refresh my memory on the Quantum Field Theory I learned 25 years ago while getting my Ph. D. At the time I did not study Chern-Simons modifications to QFT Lagrangians. ...
3
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0answers
90 views

Is a solution to the Klein-Gordon equation homeomorphic (or even diffeomorphic) to a solution of an equation with a different covariance group?

Consider some solution $\psi(x,t)$ to the linear Klein-Gordon equation: $-\partial^2_t \psi + \nabla^2 \psi = m^2 \psi$. Up to homeomorphism, can $\psi$ serve as a solution to some other equation ...
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190 views

Prequisites to learn Topological Field Theory? [closed]

Sorry for the somewhat qualitative question but what are the essential prerequisites for someone wanting to learn topological field theory from say the more physical side of things? The math side also ...
5
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1answer
282 views

Understanding Cherns-Simons-Witten Theory

I want to read about Wittens work, on Cherns-Simons theory, and relations to knots and jones polynomials. I am extremely motivated to read his paper: Quantum Field Theory and Jones polynomial. What ...
3
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0answers
101 views

Isospin and Hypercharge of the SU(2) bps monopole embedding

I am reading the paper Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups - Weinberg, Erick J . In appendix C of this paper the author states, that the solution ...
5
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1answer
166 views

Measurement of topological spin

How do you measure the topological spin of an anyon? So how could an experimental setup look like? Is topological spin an observable at all?
3
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0answers
105 views

Asymptotic limit of the two kink solution of the sine-gordon equation

I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as: ...
6
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2answers
711 views

Why are Topological Superconductors hard to make?

Topological insulators (TI) have already been made in lab. Topological superconductors (TSC), being close cousins of TI, seem harder to make. Why is that? It seems that materials in connection with ...
3
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0answers
141 views

Wilson lines, boundary conditions, surface defects of TQFTs

I asked the following question in mathematics stack exchange but I'd like to have answers from physicists too; I have been studying (extended) topological quantum field theories (in short TQFTs) from ...
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2answers
444 views

Realization of Witten-type topological quantum field theory in condensed matter physics

It is well-known that some exotic phases in condensed matter physics are described by Schwarz-type TQFTs, such as Chern-Simons theory of quantum Hall states. My question is whether there are condensed ...
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1answer
122 views

Relation between electric charge and gauge parameter of the moduli space of monopoles

I am studying about the moduli space of a 2 monopole system from Harvey's notes, and Manton's paper. In both of these, (Harvey section 6.2), after constructing the Lagrangian for a two dyons system, ...
13
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5answers
1k views

Reading list in topological QFT

I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
4
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2answers
470 views

What happens when a bare 3d topological insulator is subject to a magnetic field?

Effective field theory of 3d topological insulators (TI) predict some novel electromagnetic effects. Unfortunately it require a gapped surface which is hard to achieve experimentally. Then I have two ...
7
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0answers
168 views

Topological entanglement entropy only defined for a system in the ground state?

What happens to the topological entanglement entropy of a system, when it is driven out of its groundstate by increasing the temperature?
2
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1answer
617 views

Topological phase

Can anybody tell me, if generically any system, which is solely described by a topological field theory, resides in a topological phase? I cant find any clear notion of topological phase. Only ...
3
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1answer
208 views

Using the covariant derivative to find force between 't Hooft-Polyakov magnetic monopoles

I am reading this research paper authored by NS Manton on the Force between 't Hooft-Polyakov monopoles. I have a doubt in equation 3.6 and 3.7. We assume the gauge field for a slowly accelerating ...
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0answers
66 views

Limit of the scalar field, and potential for a soliton ( finite energy, non dissipative) solution

I want to prove that the the scalar field of the yang-mills lagrangian tends to some constant value which is a function of theta at infinity and that this value is a zero of the potential, when we ...
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1answer
213 views

What is the winding number of a magnetic monopole, and why is it conserved

I had asked a similar question about a calculation involving the winding number here. But i haven't got a satisfactory response. So, I am rephrasing this question in a slightly different manner. What ...
12
votes
1answer
619 views

Why is there no dynamics in 3D general relativity?

I heard a couple of times that there is no dynamics in 3D (2+1) GR, that it's something like a topological theory. I got the argument in the 2D case (the metric is conformally flat, Einstein equations ...
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0answers
78 views

Defects in 3+1 TFTs/2+1 CFTs

I would like to know of good pedagogic references to learn about the notion of "defects" in TFTs and CFTs. I am specially interested in 3+1 TFTs (.and probably about their relation to 2+1 CFTs..) In ...
5
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1answer
258 views

Integrating over a gauge field in the field integral formalism

I'm currently trying to study a chapter in Altland & Simons, "Condensed Matter Field Theory" (2nd edition) and I'm stuck at the end of section 9.5.2, page 579. Given the euclidean Chern-Simons ...
5
votes
1answer
222 views

what is a kink-kink-meson vertex?

These are questions I have after reading the Rajaraman's book "Solitons and instantons". So I think you must have read the book if want to answer. And also know about quantum solitons. Rajaraman ...
7
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3answers
133 views

String-theoretic significance of extended CFT

Extended TQFT and CFT have been puzzling me for while. While I understand the mathematical motivation behind them, I don't quite understand the physical meaning. In particular, it's not clear to me to ...
8
votes
2answers
178 views

Wilson Loops in Chern-Simons theory with non-compact gauge groups

VEVs of Wilson loops in Chern-Simons theory with compact gauge groups give us colored Jones, HOMFLY and Kauffman polynomials. I have not seen the computation for Wilson loops in Chern-Simons theory ...
14
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4answers
460 views

Applications of Geometric Topology to Theoretical Physics

Geometric topology is the study of manifolds, maps between manifolds, and embeddings of manifolds in one another. Included in this sub-branch of Pure Mathematics; knot theory, homotopy, manifold ...
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1answer
114 views

Quantum gravity at D = 3

Quantization of gravity (general relativity) seems to be impossible for spacetime dimension D >= 4. Instead, quantum gravity is described by string theory which is something more than quantization ...
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3answers
107 views

“tmf$(n)$ is the space of supersymmetric conformal field theories of central charge $-n$”

I read this intriguing statement in John Baez' week 197 the other day, and I've been giving it some thought. The post in question is from 2003, so I was wondering if there has been any progress in ...
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0answers
74 views

Quantum statistics of branes

Quantum statistics of particles (bosons, fermions, anyons) arises due to the possible topologies of curves in D-dimensional spacetime winding around each other What happens if we replace particles by ...
3
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1answer
94 views

Is the force between solitons with same charge always repulsive?

I know the one-dimensional case in which the force is proportional to $e^{-R}$ and the force is attractive for solitons with opposite charge and repulsive for solitons with same charge. I was ...
11
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0answers
65 views

Minimal strings and topological strings

In http://arxiv.org/abs/hep-th/0206255 Dijkgraaf and Vafa showed that the closed string partition function of the topological B-model on a Calabi-Yau of the form $uv-H(x,y)=0$ coincides with the free ...
13
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2answers
267 views

Normalization of the Chern-Simons level in $SO(N)$ gauge theory

In a 3d SU(N) gauge theory with action $\frac{k}{4\pi} \int \mathrm{Tr} (A \wedge dA + \frac{2}{3} A \wedge A \wedge A)$, where the generators are normalized to $\mathrm{Tr}(T^a ...
5
votes
2answers
490 views

Are there solitary waves in $\phi^4$ theory in 3+1 dimensions?

In 3+1 dimensions with signature +1 -1 -1 -1, $$ \mathcal{L}= \frac{1}{2}\partial^\mu\phi\partial_\mu\phi -\phi^2/2 -\phi^4/4$$ field equation: $$\square\phi+\phi+\phi^3=0$$ (check this) ...
10
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1answer
242 views

Chern-Simons theory

In Witten's paper on QFT and the Jones polynomial, he quantizes the Chern-Simons Lagrangian on $\Sigma\times \mathbb{R}^1$ for two case: (1) $\Sigma$ has no marked points (i.e., no Wilson loops) and ...
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2answers
267 views

Topological twists of SUSY gauge theory

Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this theory has 3 ...
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3answers
289 views

Geometric Langlands as a partially defined topological field theory

I have heard from several physicists that the Kapustin-Witten topological twist of $N=4$ 4-dimensional Yang-Mills theory ("the Geometric Langlands twist") is not expected to give rise to fully defined ...
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3answers
374 views

What is a nonlinear field?

I have read two possible definitions. A nonlinear field is A field taking values on a manifold. A field whose equation is nonlinear. What do you understand by a nonlinear field or a nonlinear ...
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1answer
880 views

What is a chiral field?

I have not found a clear definition of this. A teacher told me that it was a field having some constrains but that is not very convincing for me. He told me also that some examples could be skyrme ...