Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Witten index for weak supersymmetric systems: invariance under
  deformations   When a $4D$ supersymmetric theory is placed on $S^3 \times \mathbb{R}$, the
supersymmetric algebra is necessarily modified to $su(2|1)$ and we are dealing
with a weak supersymmetric system. For such systems, the excited states of the
Hamiltonian are not all paired. As a result, the Witten index Tr$\{(-1)^F
e^{-\beta H}\}$ is no longer an integer number, but a $\beta$-dependent
function.
  However, this function stays invariant under deformations of the theory that
keep the supersymmetry algebra intact. Based on the Hilbert space analysis, we
give a simple general proof of this fact. We then show how this invariance
works for two simplest weak supersymmetric quantum mechanical systems involving
a real or a complex bosonic degree of freedom.

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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex