5
votes
1answer
242 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 ...
1
vote
0answers
79 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
0answers
97 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
2answers
244 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
0answers
95 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
0answers
76 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
1answer
151 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
0answers
247 views

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

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
0answers
182 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: $$ ...
22
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 ...
4
votes
2answers
359 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 ...
31
votes
7answers
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 ...
22
votes
7answers
4k 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 ...
7
votes
1answer
455 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
2answers
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 ...
8
votes
1answer
407 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). ...
24
votes
6answers
4k 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
1answer
598 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
3answers
1k 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
1answer
290 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 ...
7
votes
0answers
644 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 ...
16
votes
6answers
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 ...
7
votes
0answers
510 views

Matrix integral identity

1) How to prove that $N\times N$ matrix integral over complex matrices $Z$ $$ \int d Z d Z^\dagger e^{-Tr Z Z^\dagger} \frac{x_1\det e^Z -x_2 \det ...
7
votes
1answer
479 views

Mirror symmetries for generalized geometries ?

For Calabi-Yau three-folds we have $\mathcal{mirror \ symmetry}$: a map that associates most Calabi-Yau three-folds $M$ another Calabi-Yau three-fold $W$ such that $ h^{1,1}(M) = h^{2,1}(W)$ and $ ...
2
votes
1answer
529 views

Are there non-supersymmetric and/or non-Calabi-Yau topological sigma models?

I am reading some aspects of Mirror Symmetry and in mirror symmetry the $N=2$ SCFT on a Calabi Yau Manifold can be divided into two sectors each of which is a topological sigma model, A-Model and ...
24
votes
3answers
2k views

What are D-branes, really?

In the past couple years, I've read many words pertaining to "D-branes" without feeling I have fully comprehended them. In broad terms, I think I get what they're about: They're supposed to serve as ...
7
votes
4answers
2k views

Generalized geometry

What role do generalized geometries (in terms of Dirac structures, for instance, symplectic, Poisson, complex, and generalized complex structures in the sense of Hitchin, Cavalcanti, and Gualtieri) ...
4
votes
1answer
432 views

Gromov-Witten and integrability 2.

This is a followup of my previous question Gromov-Witten and integrability. As I have learned from the answer (but guessed before), GW potentials of the point and $P^1$ (with different modifications) ...
7
votes
1answer
946 views

Gromov-Witten and integrability.

The generation function of the Gromow-Witten invariants (with descendants) of the point is known to be Kontsevich-Witten tau-function of KdV, partition functions of $P^1$ and equivariant $P^1$ are ...
8
votes
1answer
567 views

Virasoro constraints for the generating function of Hurwitz numbers.

Generating function of the simple Hurwitz numbers is known to be connected with Gromov-Witten potential of the point (Kontsevich $\tau$-function) (see e.g. Ian Goulden, David Jackson and Ravi Vakil). ...
3
votes
3answers
1k views

Statistical physics of string theory

Is there any connection between statistical physics and string theory, or a statistical interpretation of string theory, perhaps? I mean, the way electromagnetic forces and thermodynamic laws are ...
12
votes
2answers
794 views

Special Holonomy Groups for Lorentzian Manifolds

Let $X$ be a Riemannian manifold. If $X$ is simply connected, irreducible, and not a symmetric space then we know that the possible holonomy groups of the metric on $X$ are: 1) $O(n)$ General ...
22
votes
3answers
2k views

Topologically distinct Calabi-Yau threefolds

In dimensions 1 and 2 there is only one, respectively 2, compact Kaehler manifolds with zero first Chern class, up to diffeomorphism. However, it is an open problem whether or not the number of ...
9
votes
2answers
1k views

Higher genus closed string B-model

The closed string A-model is mathematically described by Gromov-Witten invariants of a compact symplectic manifold $X$. The genus 0 GW invariants give the structure of quantum cohomology of $X$, which ...
17
votes
1answer
1k views

What are Gromov-Witten invariants in terms of physics?

What do Gromov-Witten invariants (of say a Calabi-Yau 3-fold) represent, or what are they supposed to represent, in terms of string theory? When I compute GW invariants, am I actually computing some ...