All Questions
Tagged with mp.mathematical-physics string-theory
83 questions
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
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
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
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
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
0
votes
0
answers
242
views
how to derive this elliptic integral?
I am reading the article arXiv: 2207.09961, there are some interesting elliptic integrals, i.e. the formula (3.7) and (3.8). You can also see this image
where $p_0(z)=\sqrt{-Q_0(z)}$ and $Q_0(z)=-\...
- 1
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 "...
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
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 ...
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
1
vote
0
answers
101
views
NSR superstring as a map of supermanifolds
On one hand, I know that the NSR superstring is described by a map $\Phi: \Sigma \to X$, where $\Sigma$ is a supermanifold with local coordinates $(\sigma,\theta)=(\sigma^0,\sigma^1 | \bar{\theta},\...
- 11
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 ...
4
votes
0
answers
334
views
Axiomatic string theory?
There have been many proposal of a mathematical definition of Quantum Field Theory, for instance through Wightman or Osterwalder-Schrader axioms. Were there any efforts toward doing the same for ...
- 205
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
2
votes
0
answers
143
views
Enumerative geometry and restricted plane partitions
Donaldson-Thomas theory is an enumerative theory for virtual counts of ideal sheaves (with trivial determinant) of the structural sheaf $\mathcal{O}_{X}$ of some smooth projective manifold $X$.
There ...
- 502
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
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
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
3
votes
2
answers
615
views
On how to diagonalize a Casimir element
$\DeclareMathOperator\U{U}\DeclareMathOperator\SU{SU}\DeclareMathOperator\SO{SO}$I'm trying to read the physics paper Two Dimensional QCD as a String Theory. I'm struggling with my ignorance about ...
- 502
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
3
votes
1
answer
258
views
Supersymmetry charge $Q$ as anti-linear and anti-unitary operator
We know the supersymmetry (SUSY) charge $Q$ satisfies the following relation respect to fermion parity operator $(-1)^F$:
$$
(-1)^F Q + Q (-1)^F :=\{Q, (-1)^F \} =0
$$
which defines the anti-...
- 10.5k
5
votes
0
answers
156
views
Associating noncommutative geometries to 2D conformal field theories
I have recently been reading a bit about noncommutative geometry and string theory and it looked to be an open question (or at least this was open two decades ago) whether there are constructions ...
- 5,146
3
votes
0
answers
181
views
Lifting in String Theory and QFT
I'm posting this here instead of Physics Stack as my question is on the precise mathematical meaning of a word which is often used in the physics literature.
In theoretical physics (especially string ...
- 5,146
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 ...
- 3,282
0
votes
1
answer
280
views
Anti-symmetric operators for the Dirac or Majorana spinors
In a Zoom lecture given by a mathematical physics professor, if I recalled correctly, he explained that the in 1+1 dimensional spacetime (or 2 dimensions in short), the "action" of fermions (spinors) ...
- 2,147
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
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
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 $\beta$, $$\mathsf ...
- 1,534
6
votes
0
answers
221
views
References for superhomology
This question concerns topological string theory.
It was known sice its outset, that the BRST-cohomology ("observables") of the weakly coupled topological string B-model on a Calabi-Yau ...
- 502
3
votes
1
answer
213
views
GKO (or coset) construction - all possible highest weights $h$
I am reading the famous paper "Unitary Representations of the Virasoro and Super-Virasoro Algebras" by Goddard, Kent, Olive.
From a compact simple Lie algebra $\mathfrak{g}$ and a Lie subalgebra $\...
- 379
7
votes
1
answer
3k
views
What is the relation between BRST quantization and gauge fixing quantization
To quantize gauge field, one usually use gauge-fixing procedure and then plus ghost field, my question is what the relation between BRST quantization and gauge fixing quantization is? Because it seems ...
- 781
9
votes
3
answers
751
views
What is the definition of picture changing operation?
What is the definition of picture changing operation?
What is a standard reference where it is defined - not just used?
- 3,880
29
votes
3
answers
5k
views
Topologically distinct Calabi-Yau threefolds
In dimensions 1 and 2 there is only one, respectively 2, compact Kaehler manifolds with zero first Chern class, up to diffeomorphism. However, it is an open problem whether or not the number of ...
- 23.5k
14
votes
2
answers
3k
views
what is the stringy Kähler moduli space?
I saw the stringy moduli space mentioned in a few papers but with little no explanation. I vaguely understand it is supposed to be the moduli space of complex structures on the mirror manifold.
Could ...
- 1,889
11
votes
2
answers
2k
views
Free Boson Correlator $ \langle X(z)X(w) \rangle =- \ln |z - w| $
In physics papers, the massless free boson has a definition involving an action:
$$ S(X) = \frac{1}{8\pi} \int d\sigma^2\, \partial X \overline{\partial X}$$
The random functions $X(z)$ are ...
- 22.8k
18
votes
0
answers
549
views
Donaldson-Thomas Theory and "Quantum Foam" for Mathematicians
Let $X$ be a smooth, projective Calabi-Yau threefold. From an algebro-geometric perspective, the Donaldson-Thomas invariants $\text{DT}_{\beta, n}(X)$ are virtual counts of ideal sheaves on $X$ with ...
- 1,701
11
votes
0
answers
600
views
The Grassmannian Gr(2,8) and an E7 surprise
Are there any mathematical explanations for the following surprising facts?
$$\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
4
votes
0
answers
211
views
Bridgeland stability for restricted Kahler moduli?
Let $X$ be a simply-connected, smooth, projective Calabi-Yau threefold. To my understanding, Bridgeland introduced stability conditions on triangulated categories to give a proper mathematical ...
- 1,701
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
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
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
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
4
votes
1
answer
232
views
Are there some known identities of elliptic polylogarithms similar to the Abel identity of polylogarithm?
Let
\begin{align}
Li_2(z) = \sum_{n=1}^{\infty} \frac{z^n}{n^2}.
\end{align}
This polylogarithm satisfies the following Abel identity:
\begin{align}
& Li_2(-x) + \log x \log y \\
& + Li_2(-...
- 6,211
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
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
1
vote
0
answers
80
views
GKO construction for (Super-)Virasoro algebras
I am reading the paper "Unitary Representations of the Virasoro and Super-Virasoro Algebras" by Goddard, Kent, Olive. In many places, the authors claim results without any justification, or with ...
- 379
5
votes
0
answers
122
views
GSO projection and $H^d(M, \mathbb{Z}_2)$
This follows up the comment which suggests that asking the later 2nd part of subquestion in "GSO (Gliozzi-Scherk-Olive) projection and its Mathematics" as a new different question
GSO (...
- 10.5k
4
votes
0
answers
211
views
Open-closed string correspondence
Recently, after many years of searching for the right source, I came across the excellent lecture by Aspinwall, "Some Applications of Commutative Algebra
to String Theory", in Eisenbud's Festschrift. ...
- 441
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