The supersymmetry tag has no usage guidance.

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### What is the “quaternionic” super Brauer group?

In addition to the two reasonably well-known categories $\mathrm{SuperVect}_{\mathbb R}$ and $\mathrm{SuperVect}_{\mathbb C}$ of real and complex super vector spaces, each of which is monoidally ...

**8**

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**1**answer

432 views

### Mathematics of Chiral Rings

Let $A$ be a graded vector space, and suppose that two commuting differentials $d_1$ and $d_2$ of degree +1 act on $A$, such that $A$ equipped with either is a chain complex.
We now construct $C(A)$, ...

**2**

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**1**answer

67 views

### An intrinsic supergeometric description of the Green–Schwarz supersymmetric action

The Green-Schwarz action is a natural supersymmetric extension of the Polyakov action (with a $B$-field which I will omit in what follows since it is not relevant to the question).
For a morphism ...

**21**

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**1**answer

453 views

### Is there a symmetric monoidal 2-category “SuperDuperVect”?

Recall that the category $\mathrm{SuperVect}$, as a category, consists of pairs of vector spaces, thought of as formal direct sums $V \oplus W\,\Pi$, where $\Pi$ is the "odd line". (Called "$\Pi$" ...

**3**

votes

**1**answer

146 views

### projective representation of supergroup

In fact, I am not very clear about what I am asking, but I am looking for a concrete example of supergroup which has non-trivial projective representation(some supergroup similar to usual Lie group ...

**4**

votes

**1**answer

304 views

### Localization principle in supersymmetry

In $\S$ 9.3 of the book "Mirror symmetry" (Vafa, Zaslow eds.) the authors formulate the following general localization principle for computation of integrals with respect to both even and odd ...

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**2**answers

273 views

### Witten index non-trivial in the context of Quantum Mechanics?

Let $H$ be a self-adjoint Hamiltonian and $H$ admits a decomposition into closed operators $D,D^*$, such that we have $H = D^*D$.
I will now consider the one-dimensional case on a compact set:
So ...

**3**

votes

**0**answers

160 views

### 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 ...

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**0**answers

76 views

### 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 ...

**3**

votes

**1**answer

316 views

### A good reference for learning about super-differentiation & super-integration?

I've looked at a couple of books for basic information for super-differentiation & super-integration - Rogers Supermanifolds, and Khrennikovs Superanalysis.
Unfortunately both books lack a clear ...

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**0**answers

80 views

### 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 ...

**1**

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132 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 ...

**7**

votes

**1**answer

645 views

### wrapping M5-branes on a Riemann surface

AdS/CFT gives us a way to use geometry to study field theory! I am trying to wrap M5-branes on a Riemann surface $\Sigma_{g}$. In my problem, for a Riemann surface in 11d, the normal bundle is max ...

**9**

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**1**answer

287 views

### Is there a version of supersymmetry for homogeneous spaces?

The notion of "supersymmetry" that I am aware of proceeds as follows. One fixes a spacetime $\mathbb R^n$ and signature; I will write $\mathrm{SO}(n)$ for the corresponding group of orthogonal ...

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**0**answers

104 views

### About the massless supermultiplets in $2+1$ dimensional supersymmetry [closed]

I thought of cross-linking here this question that I had asked on physicsstackexchange.
It would be a great help if someone can answer that.

**7**

votes

**1**answer

419 views

### Matrix-tree theorem via supersymmetry (i.e. Grassman algebras)

The matrix-tree theorem states the number of spanning trees of a graph $G$ is equal to a modified determinant of the adjacency matrix or "graph Laplacian", $\Delta_G$:
$$\#\{ \text{spanning trees of ...

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**0**answers

252 views

### 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 ...

**5**

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**1**answer

372 views

### 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 ...

**22**

votes

**2**answers

737 views

### 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 ...

**23**

votes

**1**answer

1k views

### 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 ...

**8**

votes

**1**answer

922 views

### 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 ...

**3**

votes

**1**answer

1k views

### 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 ...

**0**

votes

**1**answer

796 views

### 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 ...

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votes

**2**answers

457 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 ...

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**1**answer

881 views

### 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 ...

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**2**answers

514 views

### 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? ...

**17**

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991 views

### 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 ...

**9**

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**1**answer

362 views

### 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 ...

**41**

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**11**answers

6k 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 ...

**8**

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**1**answer

435 views

### 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 ...