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.
114
questions
17
votes
1answer
552 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 ...
7
votes
0answers
507 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
1answer
330 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 ...
3
votes
0answers
93 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 ...
1
vote
0answers
89 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 ...
30
votes
4answers
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
0answers
135 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
1answer
431 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
0answers
90 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
0answers
55 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 ...
17
votes
0answers
422 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 ...
10
votes
3answers
576 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 ...
4
votes
0answers
75 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 (Gliozzi-Scherk-...
6
votes
0answers
176 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
0answers
521 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
1answer
392 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
0answers
184 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
0answers
85 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
0answers
205 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
0answers
283 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
1answer
696 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 ...
6
votes
1answer
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
0answers
271 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
1answer
657 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
1answer
243 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)...
13
votes
1answer
639 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
0answers
132 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
0answers
160 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
0answers
336 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
0answers
207 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 ...
6
votes
1answer
771 views
Does there exists a Fukaya category with no objects
... and really without even the possibility of having objects, so it's not a matter of just finding the "correct" flavour of Fukaya category to use.
Question: Does there exist interesting symplectic ...
13
votes
0answers
435 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 ...
10
votes
1answer
610 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,...
7
votes
0answers
274 views
Automorphism that the Fukaya category is “blind” to
Given a symplectic manifold $(M,\omega)$, there is a natural map
$$ Symp(M,\omega) \to Auteq(D^\pi Fuk(M,\omega))$$
which sends a symplectic automorphism to the $A_\infty$-functor it induces on the ...
5
votes
0answers
140 views
Virasoro constraints for parametrized GW invariants
Gromov-Witten invariants count isolated stable maps from Riemann surfaces to a fixed symplectic manifold $(M,\omega)$ subject to some incidence conditions. If we instead replace the target manifold ...
4
votes
1answer
155 views
Are there some known identities of elliptic polylogarithms similar to the Abel identity of polylogarithm?
Let
\begin{align}
Li_2(z) = \sum_{n=1}^{\infty} \frac{z^n}{n^2}.
\end{align}
This polylogarithm satisfies the following Abel identity:
\begin{align}
& Li_2(-x) + \log x \log y \\
& + Li_2(-...
5
votes
1answer
122 views
a matrix of Onsager-Kaufman vs Schwarz-Wu
In my earlier MO question, I was seeking for a proof for $\det A_{\infty}:=\det(I_{\infty}-M_{\infty}^2) =\sqrt[4]{1-x^2}$ where $M_n$ is the $n\times n$ matrix:
$$M_n
=\left[\frac{2i+1}{2(i+j+1)}\...
3
votes
2answers
209 views
Examples of $1$-Calabi-Yau triangulated categories
Can you give me examples of $1$-Calabi-Yau triangulated categories $D$ different from the bounded derived category of coherent sheaves on an elliptic curve? I would like moreover the numerical ...
10
votes
3answers
716 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 $\beta$, $$\mathsf ...
8
votes
2answers
1k views
What does it mean to take the diagonal of the group $SU(2) \times SU(2) $?
I am reading Witten's paper on topological field theories, in specific the topological twist in page 359. In order to perform the twist he takes the diagonal subgroup of $K = SU(2)_{\text{Right}} \...
6
votes
0answers
692 views
Understanding Segal's definition of conformal field theory
I have a fundamental problem in understanding Segal's definition of a conformal field theory:
On the one hand his monoidal CFT-functor is a formalization of the fact that, physically, the integrand ...
4
votes
1answer
267 views
BCOV's holomorphic anomaly equation at genus one
BCOV in their famous paper (http://arxiv.org/abs/hep-th/9309140) state the genus one holomorphic anomaly equation (on page 53) to be $$\partial_i \partial_{\bar{j}} F_{1} = \frac{1}{2}C_{ikl}\bar{C}^{...
5
votes
1answer
643 views
AKSZ sigma models for higher spin
The AKSZ framework constructs 2D sigma models in the BV formalism. Is there a generalization of the AKSZ approach to higher spin?
2
votes
2answers
470 views
space at the Planck scale [closed]
All models of space that I know from physics use real or complex manifolds. I was just wondering if it is still the case at the level of Planck scale. In string theory, physicists still use strings (...
3
votes
1answer
377 views
book about string theory a la Von Neumann [duplicate]
Can we summarize string theory (in its actual state) in some principles and fundamental equations like electromagnetism, general relativity, quantum mechanics and classical mechanics ?
I am looking ...
4
votes
1answer
180 views
reference for higher spin - not gravitational nor stringy
Other than the papers of Berends, Burgers and van Dam, are there any papers that study the general case of deforming a free field theory with higher spin fields to be interactive?
1
vote
1answer
221 views
Generalized spin connection and dreibein in higher spin gravity
I am studying higher spin gravity and I would like to know the mathematical and physical meaning of generalized spin connection and generalized dreibein that appear in this theory.
It is well known ...
2
votes
0answers
184 views
computation with Hilbert scheme of $n$ points on $\mathbb C^2$ [closed]
How can we show that
$$\sum_{n = 0}^\infty q^n \operatorname{char}_T S^n(\mathbb C[x,y])=
\prod_{p_1,p_2\geq 0}\frac{1}{1-t_1^{p_1}t_2^{p_2}q}$$
where $\operatorname{char}_T V$ denotes the character ...
4
votes
1answer
826 views
Mathematica package for supergravity and string theory
I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra ...
10
votes
2answers
889 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 ...
