The tag has no wiki summary.

learn more… | top users | synonyms

0
votes
0answers
75 views

Conformal welding of annuli

This question is similar to that stated in Conformal Welding Reference: Let $\Sigma$ be a 1-dim compact connected complex manifold with boundary $\partial \Sigma= \partial\Sigma^+ \cup ...
2
votes
0answers
83 views

Is there an E8 symmetry in the zero-field Ising model?

In the paper On classification of modular tensor categories by Rowell, Stong and Wang, they list the Ising modular category $I$ as having 3 objects $1$, $\sigma$ and $\psi$, with fusion rules ...
2
votes
0answers
61 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
159 views

Quantum dimension in SU(N) level k Kac-Moody algebra

The CFT of the SU(N) level k Kac-Moody current algebra has many Kac-Moody primary fields. I wonder if any one has calculated the quantum dimensions of those Kac-Moody primary fields. I know that, ...
2
votes
2answers
99 views

Distinct 2D RCFTs with the same underlying MTC

A 2d rational conformal field theory (RCFT) gives rise to a modular tensor category (MTC) equipped with a Frobenius algebra object (see, for example, http://arxiv.org/abs/hep-th/0204148). Is there an ...
1
vote
0answers
232 views

Analogues of the Monster for central charges different from 24

One way to define the Monster group is to consider a conformal field theory (CFT) corresponding to central charge $c=24$ and look at the automorphism group of its vertex operator algebra. For one of ...
5
votes
0answers
556 views

Neveu-Schwarz and Ramond sector in the free fermion CFT

My question is about the Neveu-Schwarz and the Ramond sector in the free fermion CFT. The setup is as follows. We consider two dimensional Minkowski space with a point removed $M = \mathbb{R}^{1, ...
4
votes
1answer
221 views

Verlinde Formula and Theta Function Identities

The paper Fusion rules and modular transformations in 2D conformal field theory by Erik Verlinde mentions a simple case of rational conformal field theory, where the fusion algebra is just ...
7
votes
1answer
189 views

minimal energy of affine Lie algebra reps

Let $\mathfrak g$ be a simple Lie algebra. Let $\widetilde{L\mathfrak g}$ be the universal central extension of $L\mathfrak g:=\mathfrak g[t,t^{-1}]$. Let $V_\lambda$ be a positive energy ...
7
votes
2answers
466 views

Free Boson Correlator $ \langle X(z)X(w) \rangle =- \ln |z - w| $

In physics papers, the massless free boson has a definition involving an action: $$ S(X) = \frac{1}{8\pi} \int d\sigma^2\, \partial X \overline{\partial X}$$ The random functions $X(z)$ are ...
10
votes
2answers
724 views

2d Ising model in conformal fields theory and statistical mechanics

I am not completely sure that this question is appropriate for this mathematical site. But since in the past I did get on MO couple of times nice answers to rather physical questions, I will try. ...
3
votes
2answers
223 views

In what condition is a conformal flat manifold flat?

$g^{\mu\nu}(x)=\Omega^{2}(x)g'^{\mu\nu}(x)$ is a conformal transformation. If $g'^{\mu\nu}$ is flat, what kind of $\Omega(x)$ is choosed can make $g^{\mu\nu}$ flat. We can think about any dimension ...
17
votes
3answers
550 views

Interpreting the CS/WZW correspondence

It is understood that there is a correspondence between the 3d Chern-Simons topological quantum field theory (TQFT) and the 2d Wess-Zumino-Witten conformal quantum field theory (CQFT). A good summary ...
11
votes
1answer
396 views

$\text{Rep}(D(G))$ as representation category of a vertex operator algebra

The category of representations $\text{Rep}(D(G))$ of the quantum double of a finite group is well-known to be a modular tensor category. Can these modular tensor categories also be obtained as ...
2
votes
0answers
104 views

Vertex Operators with nonlinear terms in Conformal Field Theory

Suppose that we have a simple theory described by the following Hamiltonian $$ H=\sum_{k>0}k a_k^{\dagger}a_k, $$ where $[a_k,a_{k'}^{\dagger}]=\delta_{k,k'}$. We can usually define the Vertex ...
7
votes
1answer
278 views

Duality between orbifold and quasi-Hopf algebra (twisted quantum doubles)

A quick Question: Is there some duality known between the quasi Hopf algebra $D^\omega(H)$ of a finite group $H$ to an orbifold model (such as SU(2)/$G$ or SO(3)/$G$ orbifold of some ...
21
votes
5answers
2k views

Verlinde's formula

"Verlinde's formula" predicts the dimension of the space of conformal blocks of a chiral CFT. Depending on... • which chiral CFT one considers (does one restrict to WZW models, or not?) ...
3
votes
1answer
313 views

What are Euler density and Weyl invariants?

I would like to know as to what is the definition and significance of what are called "Euler density" and "Weyl invariants" (of weight $-d$ on a $d-$manifold) Do many (which?) of them vanish when ...
3
votes
0answers
347 views

A gentle introduction to CFT [closed]

1) Which is the definition of a conformal field theory? 2) Which are the physical prerequisites one would need to start studying conformal field theories? (i.e Does one need to know supersymmetry? ...
7
votes
0answers
239 views

The space-time dimension of the N-superstring theory?

Let $\mathfrak{W}$ be the Lie algebra generated by $d_{n} = ie^{in\theta}\frac{d}{d\theta}$ and $\mathfrak{Vir} = \mathfrak{W} \oplus C \mathbb{C}$ its central extension: $$ ...
6
votes
0answers
246 views

Are there exactly solvable CFTs?

I am wondering if there are CFTs such that n-point correlation functions in them of the fields (may be the primaries or of some notion of twist fields) is exactly known. Are there such? Aren't ...
11
votes
1answer
848 views

Is this error in this paper of Langlands fixable?

The FQS criterion for the Virasoro algebra was discovered by Friedan, Qiu and Shenker (1), but the mathematicians found their proof insufficient, so that, FQS (2) and Langlands (3), published in the ...
5
votes
0answers
148 views

Proving conformal invariance of a field theory by property of its stress energy tensor.

I have a question about proving conformal invariance of a field theory by property of its stress energy tensor. In physics there is argument that when the stress-energy tensor is traceless, ...
19
votes
1answer
747 views

Has the conformally field theoretic metric on a Calabi-Yau variety been proved to exist?

Let $(X,g)$ be a compact Kähler manifold. Physics allows us to consider a supersymmetric sigma model with target $(X,g)$, which is a N=2 two-dimensional field theory. From the two-dimensional point ...
4
votes
0answers
194 views

Quantum Drinfeld-Sokolov reduction for a module

There is a well-established procedure for quantizing the Drinfeld-Sokolov reduction for an affine Lie algebra. In particular, this paper of de Boer and Tjin describes an algorithm to produce the ...
2
votes
0answers
256 views

fake Calabi-Yau threefold

(1) What is a "fake Calabi-Yau threefold"? Can I describe as a complex or symplectic manifold with trivial canonical bundle, but no compatible Kahler structure? Some mathematicians actually seem to ...
7
votes
1answer
621 views

wrapping M5-branes on a Riemann surface

AdS/CFT gives us a way to use geometry to study field theory! I am trying to wrap M5-branes on a Riemann surface $\Sigma_{g}$. In my problem, for a Riemann surface in 11d, the normal bundle is max ...
2
votes
2answers
271 views

pseutotensor category

In the paper B. Bakalov, A.D'Andrea and V.G.Kac, Theory of finite pseudoalgebras, section 3, one finds the following definition of pseudotensor category: A pseudotensor category is a class of ...
25
votes
6answers
4k views

Explanations for mathematicians, about the falsifiability (or not) of string theory [closed]

Like many other mathematicians, I think string theory very attractive. This theory has wonderfully influenced many new topics in mathematics (I myself have worked on one of them), but it's not the ...
7
votes
5answers
498 views

Example for non equivalent rational full CFTs with same modular invariant (partition function)

I am looking for a counter example which shows, that a full rational 2D CFT (with respect to a given chiral subtheory) is not characterized by its modular invariant partition function. People tell me ...
11
votes
2answers
839 views

What happens to Virasoro at c=25?

The Virasoro algebras $Vir_c$ are a family of infinite dimensional Lie *-algebras parametrized by a real number $c$, called the central charge.¹ I hear that there exist two critical values of the ...
14
votes
2answers
602 views

Is this a vertex algebroid?… What is vertex algebroid?

A couple of day ago, I was lamenting to a friend about the fact that I have no idea what vertex algebroids are. During our discussion, I came up with a guess of what a vertex algebroid might be. I'm ...
1
vote
1answer
188 views

Analytic curve on Riemann surface

Suppose there is a closed analytic curve $C$ on a Riemann surface $S$, that is the image of a map $\gamma$ from the equator $E$ of the Riemann sphere to the surface $S$ which is a restriction of a ...
12
votes
2answers
706 views

What do correlation functions compute in CFT?

I would like to understand what correlation functions compute in Conformal Field Theory in mathematics. Let me begin with basic definitions. We define a free boson field $\phi(z)$ as a formal power ...
11
votes
0answers
903 views

conformal blocks for beginners

I have given now a couple of talks that involve conformal blocks bundles on the moduli stack $\overline{\mathcal{M}}_{g,n}$, in front of a public of algebraic geometers but not specialists of the ...
1
vote
0answers
257 views

definitions of primary fields

I have come across two similar definitions of primary fields in conformal field theory. Depending on what I am doing each definition has its own usefulness. I expect both definitions to be compatible ...
1
vote
0answers
200 views

Algebra out of a set of modules of a Lie algebra? Fusion

The problem I faced is how to organize a set of finite-dimensional irreducible representations $U_\alpha$ of some simple Lie algebra $g$ into an Lie algebra $A$ that contains $g$ as a Lie subalgebra ...
4
votes
1answer
178 views

Why is there a discrepancy between the normalizations of the central terms for the commutation relations of the Virasoro versus Neveu-Schwarz Lie algebras?

Following the standard conventions in the literature, the commutation relations of the Virasoro Lie algebra are given by $$[L_m,L_n]=(m-n)L_{m+n}+\delta_{m,-n}\frac1{12}(m^3-m)c,$$ $$[c,L_n]=0.$$ ...
15
votes
1answer
432 views

Character of parity-twisted supersymmetric VOA module — question inspired by the Stolz-Teichner program

I'll begin with some background that is unnecessary for the actual question, but that might be interesting to the reader: Topological modular forms ($TMF$) is a generalized cohomology theory whose ...
18
votes
6answers
3k views

The Chern-Simons/Wess-Zumino-Witten correspondence

I have often seen a relationship being alluded to between these two theories but I am unable to find any literature which proves/derives/explains this relationship. I guess in the condensed matter ...
5
votes
1answer
369 views

Is there a fusion rule in positive characteristic?

Verlinde's fusion gives a certain "tensor product" of representations of loop groups. The category of representations of loop groups has (essentially equivalent) two incarnations. One is analytic, ...
3
votes
1answer
347 views

eigenspinors of Dirac operator

$M$ compact manifold. Let $\lambda$ be an eigenvalue for the Dirac operator of multiplicity greater than 2. I'm interested in showing the existence of two linearly independant eigenspinors $u$ and $v$ ...
4
votes
0answers
377 views

Correlation functions of complex operators

One defines the "scaling dimension" (as opposed to "engineering dimension") of an operator $\cal{O}$ as $[\cal{O}]$ such that if $\cal{O}(t^{-1}x) = t^{[\cal{O}]}\cal{O}(x)$ then the Lagrangian in ...
12
votes
1answer
526 views

What is known about the connection of positive energy representations of loop groups and modular forms

At the end of Section 14.1 in Pressley, Segal "Loop Groups" there is the remark that the partition function is a modular function in the sense that the Dedekind $\eta$ function is a modular form. I ...
44
votes
3answers
3k views

What exactly is the relation between string theory and conformal field theory?

Maybe it would be helpful for me to summarize the little bit I think know. A 2D CFT assigns a Hilbert space ${\cal H}$ to a circle and an operator $$A(X): {\cal H}^{\otimes n}\rightarrow {\cal ...
32
votes
1answer
1k views

H^4 of the Monster

The Monster group $M$ acts on the moonshine vertex algebra $V^\natural$. Because $V^\natural$ is a holomorphic vertex algebra (i.e., it has a unique irreducible module), there is a corresponding ...
18
votes
0answers
703 views

local equivalence of loop group representations

Let $G$ be a compact, simple, connected, simply connected (cscsc) Lie group, and let its smooth loop group $LG:=C^\infty(S^1,G)$. Given an interval $I\subset S^1$, we have the local loop group $$ L_IG ...
10
votes
1answer
479 views

Is there a canonical map between the cohomology of orbifold Chiral de Rham on an orbifold and the cohomology of Chiral de Rham on a crepant resolution?

The two-variable elliptic genus is a topological invariant of almost-complex manifolds that takes values in power series. These power series turn out to describe weak Jacobi forms when the manifold ...
15
votes
1answer
749 views

Codes, lattices, vertex operator algebras

At the end of "Notes on Chapter 1" in the Preface to the Third Edition of Sphere packings, lattices and groups, Conway and Sloane write the following: Finally, we cannot resist calling attention ...
2
votes
0answers
494 views

relation between AGT- conjecture and CNV-correspondence

Is there any relation between AGT conjecture 0906.3219 and the 4d-2d correspondence of 1006.3435 ? For pure SYM of $\mathcal{N}=2$ , SU(2) guage group thoery, we know the explicit instanton ...