# 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.

133
questions

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 ...

4
votes

0
answers

102
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 ...

4
votes

0
answers

159
views

### What is known about the cohomology of the U-duality group?

$\newcommand{\Es}{E_{7(7)}}\newcommand{\Z}{\mathbb Z}$Let $\Es$ denote the split form of $E_7$, which is a real Lie
group. It can be characterized as the subgroup of $\mathrm{Sp}_{56}(\mathbb R)$ ...

2
votes

0
answers

101
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 ...

8
votes

0
answers

226
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
votes

0
answers

118
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 ...

3
votes

0
answers

137
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 ...

21
votes

4
answers

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 ...

2
votes

0
answers

135
views

### Holomorphic anomaly at genus 1

For computing instantons contributions from worldsheet torus to target torus, one can evaluate zero modes contribution of genus 1 partition function given by following expression:
$$Tr(-1)^FF_LF_Rq^{...

2
votes

0
answers

132
views

### Perverse sheaves and maximal genus Gopakumar-Vafa invariants

Let $f: X \to Y$ be a proper morphism between complex varieties (the varieties as well as the map may be non-smooth) and let $\phi \in \text{Perv}(X)$ be a perverse sheaf on $X$. Given this data, it ...

26
votes

1
answer

1k
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
...

7
votes

1
answer

229
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.
...

3
votes

1
answer

170
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-...

4
votes

2
answers

220
views

### Spectral Flow Invariance for Calabi-Yau Sigma Models

I am a mathematician who has become interested in some of the mathematics of string theory, of which I am largely ignorant, so please excuse any idiocies in what follows.
If $X$ is a Calabi-Yau $d$-...

6
votes

0
answers

158
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 ...

5
votes

0
answers

138
views

### Calabi-Yau structures on dg-categories

A (smooth) dg algebra is called (left) Calabi-Yau if (see for example here)
$$ A^! = A[-n]$$
Here we use the inverse dualizing complex $A^!=\mathbf{R}\operatorname{Hom}_{(A^e)^{op}}(A,A^e)$. In ...

8
votes

1
answer

455
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 ...

3
votes

2
answers

307
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 ...

3
votes

1
answer

360
views

### Derive how the level quantization for 3d quantum Chern-Simons theory path integrals?

Let us consider abelian and non-abelian 3d quantum Chern-Simons theory path integrals:
abelian Chern-Simons theory on non-spin manifolds ---
$$
\int [DA]\exp(i \frac{k}{2\pi} \int_X (A \wedge dA ))
...

0
votes

1
answer

186
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) ...

18
votes

1
answer

836
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 ...

10
votes

1
answer

1k
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-...

6
votes

1
answer

599
views

### Why is the inertia stack of a smooth Deligne-Mumford stacks called inertia?

Let $\mathcal{X}$ be a smooth Deligne-Mumford stack. Then there is an associated stack $I\mathcal{X}$, called the inertia stack of $\mathcal{X}$.
Why is the inertia stack called "inertia"?
We can ...

2
votes

0
answers

99
views

### Possible Context for this "Siegel-like" Modular Form Construction?

The following construction of something very nearly a Siegel modular form of degree 2 arose in my research. I'm outside the worlds of automorphic forms and number theory, so I'm wondering if it ...

2
votes

0
answers

167
views

### L-infinity algebra of deformations of an L-infinity algebra?

From Schlessinger-Stasheff we know that a deformation problem should come with an associated $L_\infty$-algebra, so that gauge-equivalence classes of solutions to its Maurer-Cartan equation (the "MC ...

33
votes

4
answers

4k
views

### 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 ...

4
votes

0
answers

164
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 ...

5
votes

1
answer

545
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. ...

3
votes

1
answer

145
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 $\...

1
vote

0
answers

75
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 ...

18
votes

0
answers

486
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 ...

11
votes

3
answers

921
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 ...

5
votes

0
answers

102
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 (...

7
votes

0
answers

199
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 ...

11
votes

0
answers

561
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}}...

6
votes

1
answer

523
views

### Manifolds with negative dimension – Definition, References

Does the concept of differential manifold with negative dimension make sense, in differential geometry?
If yes, how is it defined? Do you have any reference to recommend?
My problem was born in ...

4
votes

0
answers

198
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. ...

4
votes

0
answers

94
views

### Moduli spaces for the TCFT map $HH(L) \to GW(X)$

Let $L$ be a Lagrangian submanifold of a closed symplectic manifold $X$. What I gather from Costello (see specifically $\S$2.5 there), is that one expects to have a morphism of closed TCFT's
$\tag{1}...

2
votes

0
answers

261
views

### Localization of the pushforward in equivariant cohomology

I am reading Nekrasov's paper and in page 2 he considers the $G \times T^2$ equivariant cohomology of the (compactified) moduli space $\tilde{M_k}$ of $U(N)$ instantons on $\mathbb{C}^2$. Here $G$ ...

2
votes

0
answers

299
views

### SYZ conjecture for varieties of general type or Fano

Let $X$ and $Y$ are Calabi-Yau varieties and mirror to each other. Then from HMS the Fukaya Floer category of Lagrangian intersections in $X$, is equivalent to bounded derived category of coherent ...

11
votes

1
answer

750
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 ...

7
votes

1
answer

2k
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 ...

7
votes

0
answers

330
views

### Integrality of the mirror map -- non-GKZ examples? Counterexamples?

The mirror map in mirror symmetry is the change-of-variables between the natural coordinatizations on the two mirror sides and is typically a highly-complicated transcendental function (indeed, should ...

8
votes

1
answer

732
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 ...

6
votes

1
answer

309
views

### Incorporating Divisors (D4-branes) into Donaldson-Thomas Theory?

Let $X$ be a Calabi-Yau threefold. Ordinary Donaldson-Thomas theory is formulated as a virtual count of ideal sheaves $\mathcal{I}$ with discrete invariants $\text{ch}(\mathcal{I}) = (1,0, -\beta, -n)...

18
votes

1
answer

941
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 ...

2
votes

0
answers

149
views

### Question on Hori, Iqbal and Vafa's 'D-branes and Mirror Symmetry'

In the paper mentioned above, on page 19, the physics of A-type supersymmetry is related to a Lagrangian submanifold $\gamma$ of a Kaehler manifold $X$. In particular, the phrase "...holomorphic ...

4
votes

0
answers

194
views

### Seiberg-Witten theory in 4d is categorification of Seiberg-Witten in 3d

According to Gukov et al. in this 2017 paper Seiberg-Witten theory in 4d categorifies Seiberg-Witten theory in 3d. In what sense is this phrase mentioned? I know what the process of categorification ...

5
votes

0
answers

360
views

### Mathematics of $\mathcal{N}=2$ Gauge Theory and Instantons

Someone may suggest I post this on PhysicsSE, but I would prefer to not have a physicist answer in jargon I cannot understand. In fact, the reason I'm asking this is that I'm sort of drowning in the ...

7
votes

0
answers

214
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 ...