**2**

votes

**0**answers

139 views

### computation with Hilbert scheme of $n$ points on $\mathbb C^2$ [closed]

How can we show that
$$\sum_{n = 0}^\infty q^n \operatorname{char}_T S^n(\mathbb C[x,y])=
\prod_{p_1,p_2\geq 0}\frac{1}{1-t_1^{p_1}t_2^{p_2}q}$$
where $\operatorname{char}_T V$ denotes the character ...

**4**

votes

**1**answer

372 views

### Mathematica package for supergravity and string theory

I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra ...

**7**

votes

**2**answers

426 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 ...

**2**

votes

**1**answer

154 views

### SYZ mirror symmetry for K3 surfaces

My question is essentially related to this post, but let me formulate it again. Let $f:S \rightarrow \mathbb{P}^1$ be an elliptic fibration, then this can be a SLAG fibration with respect to another ...

**10**

votes

**0**answers

165 views

### K-theoretic version of Artin-Mazur formal groups?

An Artin-Mazur formal group is, when it exists, the deformation theory of ordinary cohomology of some degree, on some algebraic variety. My question here is:
Has the generalization of the theory of ...

**1**

vote

**1**answer

128 views

### Is the structure constant additive on connected components?

Let $M$ be a Riemann surface and $\mu$ a metric on it, which could be non-compact. Moreover let $\Delta_{\mu,\,M}$ be the Laplacian on $M$ induced by $\mu$ and $\mathrm{det}^*(\Delta_{\mu,\,M})$ its ...

**18**

votes

**0**answers

535 views

### Calabi-Yau cohomology?

My question here is going to be this -- but I'll give a bit of background to explain myself in a moment:
What has been done/what results are available on Calabi-Yau cohomology in degree $n \geq 3$ ...

**8**

votes

**0**answers

235 views

### State of the art of BPS and Donaldson-Thomas invariants for toric Calabi-Yau threefolds

I am trying to understand what has been done with regards to computing BPS invariants and Donaldson-Thomas type invariants of Calabi-Yau threefolds. To make the question more focused, let's say that I ...

**15**

votes

**0**answers

353 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, it seems to me, a close relation between p-adic string theory and the refinement of ...

**5**

votes

**1**answer

320 views

### What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?

Introduction: This is slightly edited and generalised version of a question I asked on the Physics Stack Exchange website. This question has a twin brother asked here on MO, only now we consider ...

**17**

votes

**3**answers

418 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 ...

**1**

vote

**0**answers

85 views

### How can the interersection number of $2$ $D6$ branes wrapping around a CY manifold be derived?

For two intersecting $D6$ branes $a$ and $b$ wrapped around a $6$ dimensional torus $T^6 = T^2 \times T^2 \times T^2$ specified by
$$
\textrm{D6-brane a:}\, (l_1^a,l_2^a,l_3^a)
$$
$$
...

**3**

votes

**0**answers

118 views

### Physical relevance of either fundamental identity generalizing Jacobi [closed]

There are two fundamental identities for n-ary generalizations of the Jacobi identity.
One fundamental identity is right for Nambu mechanics and such, the other for L_\infty algebras as in CSFT.
Which ...

**7**

votes

**2**answers

265 views

### What is the definition of picture changing operation?

What is the definition of picture changing operation?
What is a standard reference where it is defined - not just used?

**3**

votes

**0**answers

105 views

### Where is there a treatment of double field theory other than in local coordinates?

The n-lab seems to lack a treatment of double field theory. Where is there a treatment other than in local coordinates? Or at least one which identifies the coordinates as local coordinates for a ...

**1**

vote

**0**answers

91 views

### H-flux by any other name

There are more than a few papers referring to H-flux and/or H-twist etc.
Is there anywhere a survey relating these variants?

**3**

votes

**1**answer

335 views

### The Fuchsian monodromy problem

I want to understand the argument being made from equation 6.1 to 6.5 in this paper between pages 27-28
6.2, 6.4 and 6.5 are completely out-of-the-blue to me and I have no clue as to from where they ...

**3**

votes

**1**answer

169 views

### Does fixing the reparameterization invariance of the string action correspond to some kind of orbifolding?

Does fixing the reparameterization invariance of the string action, for example by choosing the light-cone gauge
$$
X^{+} = \beta\alpha' p^{+}\tau
$$
$$
p^{+} = \frac{2\pi}{\beta} P^{\tau +}
$$
...

**5**

votes

**1**answer

412 views

### Why does closed string theory have only one dilaton field instead of $22$? [closed]

Looking at $5D$ Kaluza-Klein theory, the Kaluza-Klein metric is given by
$$
g_{mn} = \left(
\begin{array}{cc}
g_{\mu\nu} & g_{\mu 5} \\
g_{5\nu} & g_{55} \\
\end{array}
\right)
$$
...

**7**

votes

**0**answers

233 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:
$$
...

**18**

votes

**1**answer

718 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 ...

**5**

votes

**1**answer

336 views

### Proof of the general expression for anomaly in a CFT and its partition function

I think the statement is that for any dimensional CFT the following is true,
$$\langle T^{\mu}_\mu \rangle = \sum B_n I_n - 2(-1)^{d/2}AE_d,$$
where $E_d$ is the `"Euler density" and $I_n$ are ...

**8**

votes

**6**answers

905 views

### What is a branched Riemann surface with cuts?

Edit: Let me restate the main claim being made in these two papers,
Consider the "branched" Riemann surface which has "n" sheets stuck along the intervals, $[z_i, z_{i+1}]$ for $i=1,..,2N$ then it ...

**23**

votes

**6**answers

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 ...

**4**

votes

**2**answers

394 views

### CFTs corresponding to affine Lie algebras

I want to know how one can write down a CFT such that its conserved currents will satisfy some chosen (affine) Lie algebra $G$.
On the few pages leading up to page 192 in here one can see see the ...

**17**

votes

**0**answers

414 views

### On Determinants of Laplacians on Riemann Surfaces

History of the Formula: In their famous paper "On Determinants of Laplacians on Riemann Surfaces" (1986), D'Hoker and Phong computed the determinant of the Laplacian $\Delta_n^+$ on the space $T^n$ of ...

**34**

votes

**7**answers

3k views

### The Unreasonable Effectiveness of Physics in Mathematics. Why ? What/how to catch?

Starting from 80-ies the ideas either coming from physics, or by physicists themselves (e.g. Witten) are shaping many directions in mathematics. It is tempting to paraphrase E. Wigner, saying about ...

**5**

votes

**0**answers

208 views

### Seiberg-Witten curve for product SU(2)^N gauge theories

In equation 2.10 of this article, the author gives the Seiberg-Witten curve for a $U(N)$ gauge theory with $L<2N$ massive flavours with masses given by $m_i$ as:
$y^{2}=\left\langle ...

**1**

vote

**0**answers

101 views

### About the massless supermultiplets in $2+1$ dimensional supersymmetry [closed]

I thought of cross-linking here this question that I had asked on physicsstackexchange.
It would be a great help if someone can answer that.

**16**

votes

**2**answers

1k views

### Are Donaldson-Thomas invariants “A-model” or “B-model” ?

Donaldson-Thomas invariants are the (virtual) Euler characteristics of moduli spaces of elements of the derived category of coherent sheaves (with some fixed Chern class, satisfying some stability ...

**25**

votes

**7**answers

5k views

### Why does bosonic string theory require 26 spacetime dimensions?

I do not think it is possible really believe or experimentally check (now), but all modern physical doctrines suggest that out world is NOT 4-dimensional, but higher.
The least sophisticated ...

**1**

vote

**3**answers

439 views

### Computing chern classes for products of varieties

I'm currently facing the problem of computing chern classes for Varieties. More precisely the product of such varieties.
Let $C_i$ be a variety in $\mathbb{CP}^2$ given by the Weierstraß $\wp$-map.
I ...

**7**

votes

**1**answer

564 views

### what is the stringy Kähler moduli space?

I saw the stringy moduli space mentioned in a few papers but with little no explanation. I vaguely understand it is supposed to be the moduli space of complex structures on the mirror manifold.
Could ...

**6**

votes

**2**answers

1k views

### Advice on doing physics under the umbrella of mathematics and the converse

Note: This is a question directly copied from Theoretical Physics SE primarily to get the advice of people indulged in mathematics.
In the current scenario of research in QFT and string theory (and ...

**7**

votes

**0**answers

439 views

### Physicists Euler number conjecture

Physicist's Euler number conjecture says:
If $G \subset SL(n,\mathbb{C})$ is a finite group, $X=\mathbb{C}^n/G$ is the quotient space and $f:Y \rightarrow X$ a crepant resolution (always exists for ...

**8**

votes

**1**answer

424 views

### Multiple Hodge integrals and integrability

It is known that a generating function of the linear Hodge integrals is a tau function of the KP hierarchy, namely a one-parameter deformation of the Kontsevich-Witten tau-function (see Kazarian). ...

**8**

votes

**2**answers

549 views

### Elliptic genus for manifolds with boundary

Let M be a closed spin manifold of dimension $d$. One form of the elliptic genus of $M$ is
$$ F(q)=q^{-d/8} \hat A(M) {\rm ch} \otimes_{k=1/2,3/2,\cdots} \Lambda_{q^k}T \otimes_{\ell=1}^\infty ...

**44**

votes

**3**answers

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 ...

**11**

votes

**1**answer

1k views

### Donaldson-Thomas Invariants in Physics

First of all, I am sorry for there are a bunch of questions (though all related)and may not be well framed.
What are the DT invariants in physics. When one is computing DT invariants for a Calabi-Yau ...

**26**

votes

**6**answers

5k views

### Book on mathematical “rigorous” String Theory?

I've been looking high and low for a mathematical Book on String Theory. The only Book I could find was "A Mathematical Introduction to String Theory" by Albeverio, Jost, Paycha and Scarlatti. I only ...

**3**

votes

**1**answer

671 views

### vector multiplet/hypermultiplet moduli space of String Theory

What is vector multiplet and hypermultiplet moduli space associated to IIA/B string theory (or in general to a N = 2 Supersymmetric theory) ?
The vector multiplet moduli space is special Kahler while ...

**22**

votes

**3**answers

2k views

### Why is a 2d TQFT formulated as a functor?

Usual mathematical formulation of a 2d (closed) TQFT is as a functor from the category of 2-dim cobordisms between 1-dim manifolds to the category of vector spaces (satisfying various properties.)
...

**3**

votes

**0**answers

294 views

### genus one Gromov-Witten invariants of Calabi-Yau 3-folds

In
http://arxiv.org/PS_cache/hep-th/pdf/9302/9302103v1.pdf
physicists calculate (predict) genus one GW invariants of quintic (Table 1) and some other cases (Table 2).
Can any body explain to me ...

**16**

votes

**3**answers

1k views

### What do whitehead towers have to do with physics?

First let me say something that I don't completely understand, since I do not know enough physics. If I say anything wrong, someone please tell me:
For the spinning particle, there is a sigma-model, ...

**3**

votes

**1**answer

319 views

### Does $SO(32) \sim_T E_8 \times E_8$ relate to some group theoretical fact?

It is well known the existence of a T duality between the two heterotic string theories, $SO(32) \sim_T E_8 \times E_8$. Beyond the trivial point that both groups have the same dimension (496, which ...

**2**

votes

**0**answers

135 views

### Outer automorphism for $U_q(\mathfrak{su}(2|2))$

It is known that Lie superalgebra $\mathfrak{su}(2|2)$ (and only this one, not arbitrary $\mathfrak{su}(n|n)$) has the nontrivial central extension which forms an $\mathfrak{sl}_2$ triplet, let's call ...

**-1**

votes

**1**answer

576 views

### monodromy defects and Chern-Simons

In the context of string theory I recently read "The formulation of Chern-Simons theory in terms of monodromy defects can be carried through all the dualities of the present paper, leading to ...

**8**

votes

**0**answers

691 views

### triangulated/derived categories in Physics and algebraic geometry

Why do physicists care about the triangulated/derived categories?
I mean what are the problems we want to approach using the machinery of triangulated/derived categories. e.g. in homological mirror ...

**27**

votes

**3**answers

3k views

### The influence of string theory on mathematics for philosophers.

I've agreed, perhaps unwisely, to give a talk to Philosophers about string theory.
I'd like to give the philosophers an overview of the status and influence of string theory in physics, which I feel ...

**17**

votes

**6**answers

2k views

### String theory “computation” for math undergrad audience

I am giving a talk on String theory to a math undergraduate audience. I am looking for a nice and suprising mathematical computation, maybe just a surprising series expansion, which is motivated by ...