8
votes
0answers
164 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 ...
4
votes
0answers
117 views

Topological Quantum Field Theories

I've asked this on Math.SE, but with no avail. So, I decided to ask it here. I was wondering about the following after reading the Wikipedia article on TQFTs. It is said that TQFTs have vanishing ...
11
votes
3answers
300 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 ...
5
votes
1answer
118 views

Supersymmetric generalisation of the bosonic $\sigma$ model in QM

I am reading some lecture notes which demonstrate how various models in SUSY QM can be used to obtain topological invariants such as the Euler characteristic from the Witten Index. The following ...
10
votes
2answers
259 views

What is the algebraic property that corresponds to a topological term?

Warning: This question will be fairly ill-posed. I have spent a lot of time trying to make it better posed without success, so please bear with me. A single $SU(2)$ spin may be represented by the ...
7
votes
0answers
144 views

The Integral Trick and An Equality in Nakajima's Lecture

In Nekrasov et al's series papers MNS, they calculate such kinds of integral $$ \frac{E_1 E_2}{N(2\pi i)^N(E_1+E_2) }\oint d\phi_1 \wedge d\phi_2\wedge \ldots\wedge d\phi_N \prod_{i<N} (-\phi_i) ...
2
votes
0answers
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?
6
votes
2answers
222 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 : ...
9
votes
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?
6
votes
0answers
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 ...
3
votes
0answers
102 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 ...
3
votes
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: ...
13
votes
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 ...
14
votes
4answers
462 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 ...
8
votes
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 ...
11
votes
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 ...
10
votes
1answer
243 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 ...
12
votes
2answers
268 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 ...
7
votes
3answers
757 views

Group Cohomology and Topological Field Theories

I have a two-part question: First and foremost: I have been going through the paper by Dijkgraaf and Witten "Group Cohomology and Topological Field Theories". Here they give a general definition for ...