Questions tagged [supersymmetry]
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63
questions
5
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About the quantum spectrum of a certain potential.
Intuitively one understands that if one is solving the Schroedinger's equation for energies $E$ such that $\{ x \vert U(x)\leq E \}$ is compact (..is there a weaker criteria?..) then the spectrum ...
- 3,453
25
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2
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Is super-vector spaces a "universal central extension" of vector spaces?
Is there some sense in which the category $sVect$ of super-vector spaces is the "maximal non-trivial extension" of $Vect$ as a symmetric monoidal category?
Is the $\mathbb Z/2$ that shows up in the ...
- 42.5k
25
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2
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What does the Tannakian formalism reconstruct when fed the category of chain complexes?
I've recently realized that there is a gap in my understanding of the Tannakian formalism for reconstructing an (algebraic) group from its category of (finite-dimensional) representations. To warm up,...
- 53.1k
9
votes
1
answer
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I don't get a part of Bernstein's / Deligne-Morgan's proof of Poincaré-Birkhoff-Witt
Question: I am talking about the proof given on pages 50-52 of Pierre Deligne, Pavel Etingof, Daniel S. Freed, Lisa C. Jeffrey, David Kazhdan, John W. Morgan, David R. Morrison, and Edward Witten (...
- 33.2k
3
votes
1
answer
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Witten Index, letter partition function and superconformal representations.
Except in a few papers I have seen so little written about this that I am not sure I can even frame this question properly.
I would like to know of expository references and explanations on the ...
- 3,453
0
votes
1
answer
920
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Clifford Algebra and Gamma matrices: is this relation generally true for any dimension?
I expect the following relation to be vanishing. But it seems not that obvious.
$\Gamma_{ab}^{\lambda}t^at^b \Gamma_{\lambda c(d)}t^c=0$
where $t^a$ are even ghosts, "$ab$" are indices for matrix ...
- 161
3
votes
2
answers
665
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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
7
votes
1
answer
1k
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N=(2,2) supersymmetry in two-dimensional Euclidean space
Can anyone describe (or give a reference for) the 2d superspace formulation of N=(2,2) SUSY in Euclidean signature?
I'm reading Hori's excellent introduction to QFT in the book 'Mirror symmetry', and ...
- 460
17
votes
2
answers
831
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What is the conceptual significance of supercommutativity?
A $\mathbb{Z}/2\mathbb{Z}$-graded algebra is said to supercommute if $xy = (-1)^{|x| |y|} yx$; in other words, odd elements anticommute. Why is this the "right" definition of supercommutativity? (...
- 115k
19
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3
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Does the super Temperley-Lieb algebra have a Z-form?
Background Let V denote the standard (2-dimensional) module for the Lie algebra sl2(C), or equivalently for the universal envelope U = U(sl2(C)). The Temperley-Lieb algebra TLd is the algebra of ...
- 1,746
11
votes
1
answer
479
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3/4-Lie superalgebras: how much of a theory can one develop?
Let $\mathfrak{s} = \mathfrak{s}_0 \oplus \mathfrak{s}_1$ be a real Lie superalgebra. (The ground field does not matter much, but at least one formula will not work as written if the characteristic ...
- 32.8k
62
votes
11
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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 ...
- 115k
8
votes
1
answer
545
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How many embeddings are there of super-Virasoro into n Fermions?
What is the space of N=1 super-Virasoro vertex superalgebras inside the c=n/2 free fermion vertex superalgebra? [Said differently, how many Neveu-Schwartz vectors are there in n fermions?] Answers ...
- 3,083