Questions tagged [supersymmetry]
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18 questions with no upvoted or accepted answers
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What is a BPS state and why is it the cohomology of a moduli space?
The notion of a BPS state has existed in physics for a long time: I do not understand it completely, but I get the impression they are the supersymmetric analogue of ground states, and then physicists ...
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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}}...
- 1,298
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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 ...
- 502
6
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Variation Formula of APS $\eta$-Invariant and Chern-Simons Theory
In Perturbative Expansion of Chern-Simons Theory with Noncompact Gauge Group, the author proved the variation formula of the APS $\eta$-invariant. I have a few questions about their proof. I will ...
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Physical effects in supersymmetric theories of the underlying supermanifold being split or non-split?
Given an $m$-dimensional $C^{\infty}$ manifold $M$ with an $n$-dimensional vector bundle $E$ over $M$, one can use the transition functions of the manifold and the bundle to construct an ($m,n$)-...
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Localization principle in integration over supermanifolds
This post is closely related to the post Localization principle in supersymmetry
and can be considered as a continuation of it, although independent.
In § 9.3 of the book "Mirror symmetry" (K. Hori ...
- 21.8k
5
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Is the SUSY Algebra isomorphic for all Kähler Manifolds?
For a Kähler manifold, the graded algebra generated by $\partial,\overline{\partial},\partial^*,\overline{\partial}^\ast$, the Lefschetz operator, and the dual Lefschetz operator, is called the ...
- 3,399
4
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Superspace derivation of supersymmetric non-linear sigma model in Supersolutions by Deligne and Freed
I am having a little trouble understanding passage from the linear to the non-linear sigma model in Section 4.1 of Supersolutions by Deligne and Freed. Most of my confusion comes down to the ...
user482049
3
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66
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The supermoduli space of supertori with odd spin structure and metaplectic group actions
I'm trying to understand the description of the supermoduli space of supertori with odd spin structure as a quotient of the super complex upper half plane $\mathbb{H}^{1|1}$. Such a description ...
- 6,777
3
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645
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Orthosymplectic group, matrix representations
We have the orthosymplectic $osp(n,m|2k)$. The bosonic part is $so(n,m)\times sp(2k)$. The lie algebra generators are given in eg
http://cds.cern.ch/record/524737/files/0110257.pdf$
where the group ...
- 293
3
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Analytic stuctures on $\mathbb R^n$ and the nilpotent ideal of supermanifolds
I have two questions which are somewhat related:
(a) It is a well known result (of Freedman?) in differential topology that $\mathbb R^4$ has exotic smooth structures. Apparently, it is known that ...
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2
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65
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Link between Extended Supergauge Group and Twistor Theory
In a 1974 paper on supergauge transformations in four dimensions, Wess and Zumino considered an extended supergauge group which contains the conformal group as a subgroup. An interesting thing about ...
- 5,146
2
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145
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Two definitions of super-Virasoro algebra
Let $A=\mathbb C[x,\epsilon]$ where $x$ is an even variable and $\epsilon$ is an odd variable (thus $A$ is a commutative super-algebra). Let $\mathfrak g$ denote the Lie super-algebra of vector fields ...
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What exactly is the role of the mysterious manifold underlying the definition of a superspace?
In the intro to chapter 12.3 of this book about the applications of coherent states, it says that
classical spaces for bosons are real or complex vector spaces or manifolds, whereas classical spaces ...
- 418
2
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$\mathbb{Z}_2$ graded analog of row operations for supermatrices
I'm working on some research involving supermatrices, and I was wondering if there was a $\mathbb{Z}_2$ graded analog of row operations for supermatrices.
It seems to me that it makes sense to have ...
- 10.1k
1
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Existence of a minimal ideal with a specific property
Suppose that $R$ is a super-commutative ring (i.e. it is a unital $\mathbb{Z}_2$-graded ring satisfying $xy=(-1)^{|x|\cdot |y|}yx$ where $|x|$ denotes the grading degree of a homogeneous element $x\in ...
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1
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Double vector bundle vs vector bundle over supermanifolds
Double vector bundle is roughly a vector bundle over (horizontal) vector bundle.
Vector bundle is a supermanifold in a nature way (non-nature on the other way around).
My question: is a double ...
- 1,271
1
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Classification of (almost) contact structures on $S^3$
Question: Is there a classification of almost contact or contact structures on $S^3$? What is it and references?
The motivation of this question is as follows:
(1) There is one paper showing that a ...
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