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.
141 questions
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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}...
- 353
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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 ...
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q-deformation of the unitary group integral
There is a well-known orthogonality property of $U(N)$ group characters
$$
\int d U \chi_{\mu}(U)\chi_\lambda(U^\dagger V)=\delta_{\mu\lambda}\frac{\chi_\mu(V)}{\dim_\mu}
$$
where the integral is ...
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answer
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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-...
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answer
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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 ...
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1
answer
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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
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answers
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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 ...
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answer
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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
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2
answers
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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
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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 ))
...
- 2,147
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votes
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answer
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views
The Fuchsian monodromy problem
I want to understand the argument being made from equation 6.1 to 6.5 in this paper between pages 27-28
6.2, 6.4 and 6.5 are completely out-of-the-blue to me and I have no clue as to from where they ...
- 1,893
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views
What is this correspondence between composition algebras over R and superstring theories?
In the page for superstring theory, Wikipedia states:
Another approach to the number of superstring theories refers to the mathematical structure called composition algebra. In the findings of ...
- 131
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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
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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$ ...
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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
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genus one Gromov-Witten invariants of Calabi-Yau 3-folds
In
http://arxiv.org/PS_cache/hep-th/pdf/9302/9302103v1.pdf
physicists calculate (predict) genus one GW invariants of quintic (Table 1) and some other cases (Table 2).
Can any body explain to me (...
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 (...
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votes
1
answer
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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 ...
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votes
1
answer
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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
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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
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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^{...
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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 ...
- 1,701
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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 ...
- 1,701
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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 ...
- 784
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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
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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 ...
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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 ...
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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
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views
Outer automorphism for $U_q(\mathfrak{su}(2|2))$
It is known that Lie superalgebra $\mathfrak{su}(2|2)$ (and only this one, not arbitrary $\mathfrak{su}(n|n)$) has the nontrivial central extension which forms an $\mathfrak{sl}_2$ triplet, let's call ...
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Computing chern classes for products of varieties
I'm currently facing the problem of computing chern classes for Varieties. More precisely the product of such varieties.
Let $C_i$ be a variety in $\mathbb{CP}^2$ given by the Weierstraß $\wp$-map.
I ...
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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 ...
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views
Comparison between two volume forms on genus zero Teichmüller space
Consider a sphere with $n$ punctures. If you pick a holomorphic cotangent vector at each puncture, you can canonically construct a holomorphic top form in the corresponding moduli space. (The specific ...
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Divisor cohomology through spectral sequences
I don't know if it belongs here but anyway, I need to compute arithmetic genus of divisors pulled back from a Fano base space to a bundle (which may or mayn't be trivial) defined through the ...
- 11
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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},\...
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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 ...
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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
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vote
0
answers
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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
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monodromy defects and Chern-Simons
In the context of string theory I recently read "The formulation of Chern-Simons theory in terms of monodromy defects can be carried through all the dualities of the present paper, leading to ...
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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
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modular properties of macmahon function?
How does the MacMahon function for counting plane partitions
$M(q) = \frac{1}{(1-q^n)^n}$
behave under modular transformations?
For instance for $q= e^{2 \pi i \tau}$ where $\tau \rightarrow -1/\tau$.
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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)=-\...
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