All Questions
Tagged with supersymmetry dg.differential-geometry
8 questions
6
votes
0
answers
217
views
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 ...
- 615
12
votes
1
answer
621
views
supersymmetry and the de Rham complex
In Alvarez-Gaume's paper "Supersymmetry and the index theorem" there is
given a certain supersymmetric Lagrangian whose quantization, apparently, leads to the de Rham Laplacian on the exterior ...
- 293
6
votes
0
answers
217
views
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 ($m,n$)-...
- 418
19
votes
7
answers
2k
views
Supermanifolds — elementary introduction?
I am looking for an elementary but mathematically precise introductory text on supermanifolds in a modern differential geometric setting.
Elementary in the sense that there is plenty of motivation for ...
- 3,873
2
votes
0
answers
234
views
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
1
vote
0
answers
222
views
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 ...
- 857
3
votes
2
answers
682
views
Change of coordinates introduced through dx
Hi,
I have a superspace spanned by 4 commuting coordinates + 2 anti-commuting ones $\{x^\mu,\theta^\alpha\}$, I have to do the change of coordinates $dx^\mu\to dy^\mu= dx^\mu+d\theta^\alpha \eta_\...
- 733
66
votes
11
answers
11k
views
Why is the exterior algebra so ubiquitous?
The exterior algebra of a vector space V seems to appear all over the place, such as in
the definition of the cross product and determinant,
the description of the Grassmannian as a variety,
the ...
- 118k