Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Yuji Tachikawa, Yuji Tachikawa, , ,
| Summary:
We construct a new invariant of two-dimensional $mathcalN=(0,1)$
supersymmetric quantum field theories (SQFTs), under a couple of assumptions on
the general properties of such SQFTs motivated by considerations in heterotic
string theory. This new invariant is in addition to the known ‘primary’
invariants, i.e. the ordinary elliptic genus and the mod-2 elliptic genus, and
the known ‘secondary’ invariant, which can be considered as an SQFT analog of
the Atiyah-Patodi-Singer $eta$-invariant when its continuous variation
vanishes.
We also define a spectral invariant of supercharge more generally by the
integration of the expectation value of the supercharge over the fundamental
region of $mathrm SL(2,mathbbZ)$. With this spectral invariant, we
construct a spectral pairing which can be used to systematically detect all the
known invariants, including the new one we introduce in the first half of this
paper.
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