6
votes
1answer
114 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 ...
3
votes
0answers
78 views

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

This is the sine-Gordon action: $$ \frac{1}{4\pi} \int_{ \mathcal{M}^2} dt \; dx \; k\, \partial_t \Phi \partial_x \Phi - v \,\partial_x \Phi \partial_x \Phi + g \cos(\beta_{}^{} \cdot\Phi_{}) $$ ...
5
votes
0answers
60 views

Topology-dependent groud state degeneracy of $B \wedge F + B \wedge B$ and $B \wedge F + B \wedge B \wedge B$

There are some examples of topological BF theory with extra terms allow it still being topological. See this Ref. paper In 4d (3+1D), we have the trace of: $$ \int\frac{k}{2\pi}\text{Tr}[B \wedge F + ...
12
votes
1answer
227 views

Self-dual Maxwell equations, the second homology group, and topological invariants of a four manifold

In Witten's paper Quantum Field Theory and the Jones Polynomial, he mentioned that: Geometers have long known that (via de Rham theory) the self-dual and anti-self-dual Maxwell equations are ...
4
votes
1answer
93 views

Gravitational Chern-Simons theory for bosons and fermions

Q1: What is the difference of boson and fermions for their Gravitational Chern-Simons theory? I suppose in general if the metric is not flat, we have vierbein ${e_{\hat{b}}}^{\nu}$, with $$ ...
5
votes
1answer
66 views

Quantized coefficients of Chern-Simons action and F $\wedge$ F $\wedge \dots$

We know that for U(1) gauge field Chern-Simons action in 2+1 Dim(ension), we have an action $$ S=\alpha \int A \wedge dA $$ with $\alpha=k/(4\pi)$ for a proper level quantization. Here $k$ is the ...
8
votes
0answers
223 views

p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)

I am going to ask a question, at the end below, on whether anyone has tried to make more explicit what should be a close relation between p-adic string theory and the refinement of the superstring ...
13
votes
3answers
378 views

about the Atiyah-Segal axioms on topological quantum field theory

Trying to go through the page on Topological quantum field theory - The original Atiyah-Segal axioms - "Let $\Lambda$ be a commutative ring with 1, Atiyah originally proposed the axioms of a ...
6
votes
1answer
220 views

Topological ground state degeneracy of SU(N), SO(N), Sp(N) Chern-Simons theory

We know that level-k Abelian 2+1D Chern-Simons theory on the $T^2$ spatial torus gives ground state degeneracy($GSD$): $$GSD=k$$ How about $GSD$ on $T^2$ spatial torus of: SU(N)$_k$ level-k ...
3
votes
1answer
114 views

electric, magnetic and level quantization for a SU(N), SO(N) and a compact U(1) Chern-Simons theory

Imagine three different worlds describe by three theories (I), (II), (III). Theory (I) - compact U(1) Chern-Simons: A compact U(1) Chern-Simons theory with magnetic monopole charges $m_1$. ...
10
votes
0answers
188 views

Orbifold CFT of SU(2)/G and SO(3)/G

In this paper by Dijkgraaf, Vafa, Verlinde, Verlinde, orbifold CFT is discussed. In that paper, it outlined that orbifold CFT provides a way to generate the new theories from the old known ones. ...
16
votes
1answer
718 views

Zero modes ~ zero eigenvalue modes ~ zero energy modes?

There have been several Phys.SE questions on the topic of zero modes. Such as, e.g., zero-modes (What are zero modes?, Can massive fermions have zero modes?), majorana-zero-modes (Majorana zero ...
2
votes
0answers
60 views

About the duality when embedding Gopakumar-Vafa into superstring theory

Vafa proposed a duality when embedding the Gopakumar-Vafa duality into superstring theory. Vafa's duality is about a correspondence N=1 supersymmetric gauge theory and superstring propagating on ...
2
votes
0answers
117 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?
3
votes
1answer
92 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 ...
6
votes
2answers
253 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
votes
1answer
104 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
votes
1answer
201 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 ...
5
votes
0answers
80 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 ...
7
votes
3answers
152 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 ...
10
votes
0answers
80 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 ...
11
votes
0answers
76 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 ...
21
votes
2answers
2k views

Is there a T-dual of Witten's twistor topological string theory?

In late 2003, Edward Witten released a paper that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four ...