All Questions
Tagged with string-theory mp.mathematical-physics
83 questions
9
votes
3
answers
751
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?
- 3,880
2
votes
0
answers
137
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 ...
- 3,880
1
vote
0
answers
94
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?
- 3,880
3
votes
1
answer
353
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
$$
X^{+} = \beta\alpha' p^{+}\tau
$$
$$
p^{+} = \frac{2\pi}{\beta} P^{\tau +}
$$
...
- 418
6
votes
1
answer
629
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
$$
g_{mn} = \left(
\begin{array}{cc}
g_{\mu\nu} & g_{\mu 5} \\
g_{5\nu} & g_{55} \\
\end{array}
\right)
$$
...
- 418
9
votes
0
answers
321
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:
$$
[L_m,L_n]=(m-n)L_{m+n}+\...
31
votes
6
answers
8k
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 ...
5
votes
2
answers
847
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 ...
- 3,541
51
votes
9
answers
9k
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 "...
59
votes
7
answers
18k
views
Mathematician trying to learn string theory
I'm a mathematician. I want to be able to read recent ArXiv postings on high energy physics theory (String theory) (and perhaps be able to do research). I want to understand compactifications, ...
36
votes
9
answers
18k
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 ...
- 24.9k
14
votes
2
answers
3k
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 ...
- 1,889
5
votes
2
answers
2k
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
1
answer
566
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). ...
- 1,343
44
votes
6
answers
12k
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 ...
4
votes
1
answer
1k
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 ...
- 3,218
29
votes
3
answers
3k
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.)
...
- 6,133
4
votes
2
answers
752
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 ...
- 437
8
votes
0
answers
1k
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 ...
23
votes
6
answers
3k
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 ...
- 3,202
8
votes
1
answer
1k
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 e^{AZ^\dagger}}{\det(1-x_1e^Z)\det(1-x_2e^{AZ^\dagger}...
- 1,343
7
votes
1
answer
675
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 $ h^{...
- 165
2
votes
1
answer
699
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 B-...
- 3,218
36
votes
3
answers
5k
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 ...
- 1,415
9
votes
4
answers
4k
views
Role for generalized geometries in string theory
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) ...
- 165
6
votes
1
answer
577
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) ...
- 1,343
10
votes
2
answers
2k
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 ...
- 1,343
8
votes
1
answer
842
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). ...
- 1,343
4
votes
3
answers
3k
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 ...
- 2,383
12
votes
2
answers
1k
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 ...
- 2,097
29
votes
3
answers
5k
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 ...
- 23.5k
15
votes
2
answers
2k
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 ...
- 21k
25
votes
1
answer
4k
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 ...
- 21k