Questions tagged [string-theory]

A class of theories that attempt to explain all existing particles (including force carriers) as vibrational modes of extended objects, such as the 1-dimensional fundamental string.

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66
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3answers
8k 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 H}^{\...
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7answers
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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, ...
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9answers
7k 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 "...
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6answers
9k 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 ...
36
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9answers
15k 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 ...
34
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3answers
3k 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 ...
31
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4answers
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Mathematical uses of string theory

It is widely believed that correctness of string theory as a physical theory will not be decided in the near future. Regardless whether this will turn out to be correct or not, mathematical concepts ...
29
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6answers
7k 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
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3answers
4k 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 ...
28
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3answers
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.) ...
27
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3answers
4k 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 ...
27
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2answers
908 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 ...
25
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0answers
966 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 $n \geq 3$ (...
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2answers
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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 ...
24
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1answer
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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 ...
24
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1answer
847 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 ...
23
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3answers
2k 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, ...
23
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0answers
1k 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 ...
22
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4answers
2k 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 ...
21
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6answers
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 ...
20
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3answers
2k 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 ...
20
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1answer
983 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 ...
19
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1answer
2k views

M24 moonshine for K3

There are recent papers suggesting that the elliptic genus of K3 exhibits moonshine for the Mathieu group $M_{24}$ (http://arXiv.org/pdf/1004.0956). Does anyone know of constructions of $M_{24}$ ...
17
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1answer
703 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 ...
17
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1answer
796 views

Do all $\mathcal{N}=2$ Gauge Theories “Descend” from String Theory?

I asked this on PhysicsSE, but I think it also fits here as it's related to algebro-geometric connections to string and gauge theory. I'm thinking about the beautiful story of "geometrical ...
17
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0answers
441 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 ...
16
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1answer
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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 ...
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2answers
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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 ...
14
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2answers
2k 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 ...
13
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0answers
468 views

Open conjectures on the Fukaya category coming from physics

This is a slightly vague question (for which I apologize in advance): can somebody give examples to open conjectures on the behavior of the $Fuk(M,\omega)$ that come from string theory and can be ...
13
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0answers
494 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 ...
12
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2answers
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 ...
12
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0answers
275 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 ...
11
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1answer
732 views

Large Complex Structure Limit of Calabi-Yau family and uniqueness of limit

Let $\mathcal X$ be a smooth complex manifold of dimension $n+1$. We say $\mathcal X \to ∆$ is a large complex structure limit if and only if it’s maximal unipotent degeneration . $T: H^n(\mathcal ...
11
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0answers
539 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}}...
10
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3answers
757 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 ...
10
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2answers
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 ...
10
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2answers
990 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 ...
10
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3answers
742 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
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1answer
660 views

Instanton Moduli Space on ALE Spaces

I asked this on MathStackExchange and was instructed it would be better here. I've recently been learning about moduli spaces of instantons on $\mathbb{C}^{2}=\mathbb{R}^{4}$. From what I can gather,...
9
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4answers
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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) ...
9
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3answers
647 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?
9
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2answers
675 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 S_{q^\...
9
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1answer
930 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-...
9
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0answers
287 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
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6answers
2k 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 is ...
8
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1answer
860 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 ...
8
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1answer
567 views

Cartographic group and flat stringy connection

There's a literature about dessins d'enfants (including my previous question here), and one amazing thing about them is that absolute Galois group Gal Q acts on ...
8
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2answers
1k 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}} \...
8
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1answer
767 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). ...