# Questions tagged [supersymmetry]

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### Chain rule for the superderivative

A one dimensional complex supermanifold $X$ is locally described by an ordinary complex coordinate $z$ and an anticommuting coordinate $\theta$, $\theta^2 = 0$. The superderivative is the square root ...
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### 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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### Notation on Supergeometry — parity

I know that given a manifold $M$ and its corresponding tangent bundle $TM$ we can call $\Pi TM$ the space of forms parametrized (via charts) by $\{x_i\}_{i=1,\dotsc,n}$ and its corresponding cotangent ...
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### Spectral Flow Invariance for Calabi-Yau Sigma Models

I am a mathematician who has become interested in some of the mathematics of string theory, of which I am largely ignorant, so please excuse any idiocies in what follows. If $X$ is a Calabi-Yau $d$-...
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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 ...
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### Sufficient conditions for unitarity of a representation of a Lie Superalgebra

Suppose we have a Lie superalgebra with triangular decomposition: \begin{equation} \mathfrak{g} = \mathfrak{g}^{+} \oplus \mathfrak{g}^{0} \oplus \mathfrak{g}^{-} \end{equation} I've seen it stated ...
149 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 ...
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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 ...
382 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 ...
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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 ...
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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,...
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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 (...
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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 ...
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 ...
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_\...