All Questions
Tagged with string-theory mp.mathematical-physics
83 questions
5
votes
1
answer
664
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?
- 3,880
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
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
5
votes
0
answers
165
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 ...
- 1,981
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
4
votes
1
answer
1k
views
vector multiplet/hypermultiplet moduli space of String Theory
What is vector multiplet and hypermultiplet moduli space associated to IIA/B string theory (or in general to a N = 2 Supersymmetric theory) ?
The vector multiplet moduli space is special Kahler while ...
- 3,218
4
votes
3
answers
3k
views
Statistical physics of string theory
Is there any connection between statistical physics and string theory, or a statistical interpretation of string theory, perhaps? I mean, the way electromagnetic forces and thermodynamic laws are ...
- 2,383
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
4
votes
1
answer
185
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?
- 3,880
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
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
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
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
3
votes
1
answer
447
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 ...
- 277
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
3
votes
1
answer
354
views
Does fixing the reparameterization invariance of the string action correspond to some kind of orbifolding?
Does fixing the reparameterization invariance of the string action, for example by choosing the light-cone gauge
$$
X^{+} = \beta\alpha' p^{+}\tau
$$
$$
p^{+} = \frac{2\pi}{\beta} P^{\tau +}
$$
...
- 418
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
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
3
votes
0
answers
343
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 $G$ ...
- 587
3
votes
0
answers
150
views
Physical relevance of either fundamental identity generalizing Jacobi [closed]
There are two fundamental identities for n-ary generalizations of the Jacobi identity.
One fundamental identity is right for Nambu mechanics and such, the other for L_\infty algebras as in CSFT.
Which ...
- 3,880
2
votes
2
answers
508
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 (...
- 205
2
votes
1
answer
279
views
Is the structure constant additive on connected components?
This is the reanimation of a question which already got an answer, that I did not fully understand. Coming back to it, after let it sit in a corner for some time, I keep not getting the point. I would ...
2
votes
1
answer
700
views
Are there non-supersymmetric and/or non-Calabi-Yau topological sigma models?
I am reading some aspects of Mirror Symmetry and in mirror symmetry the $N=2$ SCFT on a Calabi Yau Manifold can be divided into two sectors each of which is a topological sigma model, A-Model and B-...
- 3,218
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
2
votes
0
answers
349
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 ...
user21574
2
votes
0
answers
175
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 ...
- 1,155
2
votes
0
answers
137
views
Where is there a treatment of double field theory other than in local coordinates?
The n-lab seems to lack a treatment of double field theory. Where is there a treatment other than in local coordinates? Or at least one which identifies the coordinates as local coordinates for a ...
- 3,880
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
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
1
vote
0
answers
101
views
How can the interersection number of $2$ $D6$ branes wrapping around a CY manifold be derived?
For two intersecting $D6$ branes $a$ and $b$ wrapped around a $6$ dimensional torus $T^6 = T^2 \times T^2 \times T^2$ specified by
$$
\textrm{D6-brane a:}\, (l_1^a,l_2^a,l_3^a)
$$
$$
\textrm{D6-...
- 418
1
vote
0
answers
94
views
H-flux by any other name
There are more than a few papers referring to H-flux and/or H-twist etc.
Is there anywhere a survey relating these variants?
- 3,880
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
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