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Boundary conditions and localization on AdS. Part I

David, Justin R and Gava, Edi and Gupta, Rajesh Kumar and Narain, Kumar (2018) Boundary conditions and localization on AdS. Part I. In: JOURNAL OF HIGH ENERGY PHYSICS (9).

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Official URL: http://dx.doi.org/10.1007/JHEP09(2018)063

Abstract

We study the role of boundary conditions on the one loop partition function the N = 2 chiral multiplet of R-charge Delta on AdS(2) x S-1. The chiral multiplet is coupled to a background vector multiplet which preserves supersymmetry. We implement normalizable boundary conditions in AdS(2) and develop the Green's function method to obtain the one loop determinant. We evaluate the one loop determinant for two different actions: the standard action and the Q-exact deformed positive definite action used for localization. We show that if there exists an integer n in the interval D : (Delta-1/2L, Delta/2L), where L being the ratio of radius of AdS(2) to that of S-1, then the one loop determinants obtained for the two actions differ. It is in this situation that fields which obey normalizable boundary conditions do not obey supersymmetric boundary conditions. However if there are no integers in D, then fields which obey normalizable boundary conditions also obey supersymmetric boundary conditions and the one loop determinants of the two actions precisely agree. We also show that it is only in the latter situation that the one loop determinant obtained by evaluating the index of the D-10 operator associated with the localizing action agrees with the one loop determinant obtained using Green's function method.

Item Type: Journal Article
Additional Information: Copy right for this article belong to SPRINGER
Keywords: Extended Supersymmetry; Field Theories in Lower Dimensions; Supersymmetric Gauge Theory
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 10 Oct 2018 15:15
Last Modified: 10 Oct 2018 15:15
URI: http://eprints.iisc.ac.in/id/eprint/60854

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