2d Wall-Crossing, R-twisting, and a Supersymmetric Index

Source: arXiv

ABSTRACT Starting from N=2 supersymmetric theories in 2 dimensions, we formulate a novel time-dependent supersymmetric quantum theory where the R-charge is twisted along the time. The invariance of the supersymmetric index under variations of the action for these theories leads to two predictions: In the IR limit it predicts how the degeneracy of BPS states change as we cross the walls of marginal stability. On the other hand, its equivalence with the UV limit relates this to the spectrum of the U(1) R-charges of the Ramond ground states at the conformal point. This leads to a conceptually simple derivation of results previously derived using tt* geometry, now based on time-dependent supersymmetric quantum mechanics. Comment: 28 pages

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    ABSTRACT: We give a summary of a talk delivered at the 2012 International Congress on Mathematical Physics. We review d=4, N=2 quantum field theory and some of the exact statements which can be made about it. We discuss the wall-crossing phenomenon. An interesting application is a new construction of hyperkahler metrics on certain manifolds. Then we discuss geometric constructions which lead to exact results on the BPS spectra for some d=4, N=2 field theories and on expectation values of -- for example -- Wilson line operators. These new constructions have interesting relations to a number of other areas of physical mathematics.
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    ABSTRACT: We present a unifying theme relating BPS partition functions and superconformal indices. In the case with complex SUSY central charges (as in N=2 in d=4 and N=(2,2) in d=2) the known results can be reinterpreted as the statement that the BPS partition functions can be used to compute a specialization of the superconformal indices. We argue that in the case with real central charge in the supersymmetry algebra, as in N=1 in d=5 (or the N=2 in d=3), the BPS degeneracy captures the full superconformal index. Furthermore, we argue that refined topological strings, which captures 5d BPS degeneracies of M-theory on CY 3-folds, can be used to compute 5d supersymmetric index including in the sectors with 3d defects for a large class of 5d superconformal theories. Moreover, we provide evidence that distinct Calabi-Yau singularities which are expected to lead to the same SCFT yield the same index.
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    ABSTRACT: We study the $ \mathcal{N} = 2 $ gauge theories obtained by engineering the Type IIB superstring on the quasi-homogeneous elements of Arnold’s list of bimodal singularities. All these theories have finite BPS chambers and we describe, along the lines of arXiv:1107.5747, the algebraically obvious ones. Our results leads to the prediction of 11 new periodic Y -systems, providing additional evidence for the correspondence in between thermodinamical Bethe ansatz periodic Y -systems and $ \mathcal{N} = 2 $ superconformal theories with a finite BPS chamber whose chiral primaries have dimensions of the form N/ℓ.
    Journal of High Energy Physics 11/2011; 2011(11). · 6.22 Impact Factor

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