All Questions
Tagged with string-theory mp.mathematical-physics
83 questions
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, ...
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 "...
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 ...
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
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
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 ...
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
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
28
votes
1
answer
2k
views
In M-theory, what can hypothesis H tell us that quantization in ordinary cohomology cannot?
In classical field theory, many fields and related objects are described as differential
forms. For example, in electromagnetism, the field $F := B - \mathrm dt\wedge E$ is a 2-form, and Maxwell's
...
- 6,881
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
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
21
votes
4
answers
3k
views
Mathematical predictions of AdS/CFT
What sorts of mathematical statements are predicted by the AdS/CFT correspondence?
My "understanding" (term used very loosely) is that this correspondence isn't a mathematically rigorous ...
- 1,404
20
votes
1
answer
3k
views
What are "branes", and why do they form a category?
I've been trying to read Kapustin–Witten - Electric–Magnetic Duality And The Geometric Langlands Program recently, as someone whose mathematical interests are in the Langlands program. I have some ...
- 3,309
19
votes
1
answer
1k
views
Anomaly in QFT physics v.s. determinant line bundle
In a quantum field theory (QFT) lecture, a math-physics professor explains the anomaly in physics, say the non-invariance of the partition function of an anomalous theory under background field ...
- 2,147
18
votes
0
answers
549
views
Donaldson-Thomas Theory and "Quantum Foam" for Mathematicians
Let $X$ be a smooth, projective Calabi-Yau threefold. From an algebro-geometric perspective, the Donaldson-Thomas invariants $\text{DT}_{\beta, n}(X)$ are virtual counts of ideal sheaves on $X$ with ...
- 1,701
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
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
14
votes
0
answers
577
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 ...
- 509
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
11
votes
3
answers
1k
views
In Gromov-Witten theory, why is the string coupling constant weighted by $2g-2$?
Let $X$ be a Calabi-Yau threefold and let us fix a homology class $\beta\in H_2(X,\mathbb Z)$, just for simplicity. The generating series of Gromov-Witten invariants of $X$ in class $\beta$, $$\mathsf ...
- 1,534
11
votes
2
answers
2k
views
Free Boson Correlator $ \langle X(z)X(w) \rangle =- \ln |z - w| $
In physics papers, the massless free boson has a definition involving an action:
$$ S(X) = \frac{1}{8\pi} \int d\sigma^2\, \partial X \overline{\partial X}$$
The random functions $X(z)$ are ...
- 22.8k
11
votes
3
answers
1k
views
Navier-Stokes fluid dynamics, Einstein gravity and holography
There was some activity a while ago, like 10 years ago, string theoreists try to relate
the fluid dynamics, for example, governed by Navier-Stokes equation,
to
the Einstein gravity, and its ...
- 10.5k
11
votes
1
answer
2k
views
Vafa-Witten invariants for mathematicians
As Richard Thomas has written (we paraphrase just slightly), mathematical physicists Vafa and Witten introduced new "invariants" of four-dimensional spaces in a paper:
A Strong Coupling Test of S-...
- 10.5k
11
votes
0
answers
600
views
The Grassmannian Gr(2,8) and an E7 surprise
Are there any mathematical explanations for the following surprising facts?
$$\int_{Gr(2,8)} c_{\text{top}}(TX(-2)) = 6556 = \frac{1}{2} \deg(E_7/P(\alpha_7)) + 1,$$
and
$$\int_{Gr(2,6)} c_{\text{top}}...
- 1,298
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
10
votes
0
answers
266
views
Physical Approach to Knot Categorification
Some recent work by Aganagic on knot categorification, Knot Categorification from Mirror Symmetry, Part II: Lagrangians, discusses two categorical approaches to categorification of quantum link ...
- 5,146
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
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
9
votes
1
answer
1k
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 ...
- 4,829
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:
$$
[L_m,L_n]=(m-n)L_{m+n}+\...
8
votes
2
answers
2k
views
What does it mean to take the diagonal of the group $SU(2) \times SU(2) $?
I am reading Witten's paper on topological field theories, in specific the topological twist in page 359. In order to perform the twist he takes the diagonal subgroup of $K = SU(2)_{\text{Right}} \...
- 587
8
votes
1
answer
842
views
Virasoro constraints for the generating function of Hurwitz numbers.
Generating function of the simple Hurwitz numbers is known to be connected with Gromov-Witten potential of the point (Kontsevich $\tau$-function) (see e.g. Ian Goulden, David Jackson and Ravi Vakil). ...
- 1,343
8
votes
1
answer
566
views
Multiple Hodge integrals and integrability
It is known that a generating function of the linear Hodge integrals is a tau function of the KP hierarchy, namely a one-parameter deformation of the Kontsevich-Witten tau-function (see Kazarian). ...
- 1,343
8
votes
1
answer
805
views
How to construct the mirror partner of a blowup?
Question: Let's assume we have a pair $(X,\check{X})$ that are mirror dual to each other in the sense of Homological mirror symmetry (EDIT: this does not have to be CY n-folds, but can also be a Fano ...
- 1,981
8
votes
1
answer
665
views
References for quivers and derived categories of coherent sheaves for a string theory student
I'm a student mostly from physics knowledge hoping to learn about the math involved the string theory paper Topological Quiver Matrix Models and Quantum Foam.
Context: The topological string theory ...
- 502
8
votes
1
answer
1k
views
Matrix integral identity
1) How to prove that $N\times N$ matrix integral over complex matrices $Z$
$$
\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
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 ...
7
votes
1
answer
3k
views
What is the relation between BRST quantization and gauge fixing quantization
To quantize gauge field, one usually use gauge-fixing procedure and then plus ghost field, my question is what the relation between BRST quantization and gauge fixing quantization is? Because it seems ...
- 781
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
7
votes
1
answer
297
views
Affine Kac-Moody algebra from quantum group exchange algebra
In `Hidden Quantum Groups Inside Kac-Moody Algebra', by Alekseev, Faddeev, and Semenov-Tian-Shansky, a relationship between quantum groups and affine Kac-Moody algebras is shown for the WZW model.
...
- 1,155
7
votes
0
answers
239
views
GSO (Gliozzi-Scherk-Olive) projection and its Mathematics?
GSO (Gliozzi-Scherk-Olive) projection is an ingredient used in constructing a consistent model in superstring theory. The projection is a selection of a subset of possible vertex operators in the ...
- 10.5k
7
votes
0
answers
225
views
Relation between Donaldson invariants and GW invariants
What is known about the relation of Donaldson invariants on a complex surface $\Sigma$ and GW invariants (or equivalent) of local Calabi-Yau 3folds such as the canonical bundle of $\Sigma$? (if any of ...
- 661
6
votes
2
answers
2k
views
Freeman Dyson's approach to string theory [closed]
Context:
In celebrating the centenary of Ramanujan's birth, Freeman Dyson presented the following career advice for talented young physicists [1]:
My dream is that I will live to see the day when our ...
- 3,871
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
6
votes
1
answer
726
views
Degree-3 curves on the Calabi–Yau quintic
Robbert Dijkgraaf said,1
concerning the simplest
Calabi–Yau space, the quintic:
"A classical result from the 19th century states that the number of lines — degree-one curves — is equal to 2,875. ...
- 151k
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
6
votes
0
answers
221
views
References for superhomology
This question concerns topological string theory.
It was known sice its outset, that the BRST-cohomology ("observables") of the weakly coupled topological string B-model on a Calabi-Yau ...
- 502
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 ...
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
5
votes
1
answer
158
views
a matrix of Onsager-Kaufman vs Schwarz-Wu
In my earlier MO question, I was seeking for a proof for $\det A_{\infty}:=\det(I_{\infty}-M_{\infty}^2) =\sqrt[4]{1-x^2}$ where $M_n$ is the $n\times n$ matrix:
$$M_n
=\left[\frac{2i+1}{2(i+j+1)}\...
- 43.2k