Abstract
Abstract We study quantum aspects of the target space of the non-linear sigma model, which is a low-energy effective theory of the gauged linear sigma model (GLSM). As such, we especially compute the exact sphere partition function of the GLSM for KK$5$-branes whose background geometry is a Taub–NUT space, using the supersymmetric localization technique on the Coulomb branch. From the sphere partition function, we distill the world-sheet instanton effects. In particular, we show that, concerning the single-centered Taub–NUT space, instanton contributions exist only if the asymptotic radius of the $S^1$ fiber in the Taub–NUT space is zero.
Highlights
In string theory, lots of spatially extended objects, dubbed as branes, are included as dynamical degrees of freedom
It is known that in the context of gauged linear sigma model (GLSM), the background geometries of the H-monopoles and the KK5-branes are corrected by the world-sheet instantons [5, 43], which means that one can deal with the world-sheet instantons based on GLSM that allows us to conduct analyses from the view point of string
We have considered GLSM for the KK5-branes [6] together with the introduction of the moduli specifying the location of the branes in the target space [10]
Summary
Lots of spatially extended objects, dubbed as branes, are included as dynamical degrees of freedom Amongst all these branes, D-branes are the standard branes while there exist exotic branes characterized by co-dimensions and the brane tension; they are intimately related each other through various duality transformations [1,2,3]. A well-known example is a smeared NS5brane (an H-monopole) that is T-dual to a KK5-brane (a Kaluza-Klein monopole) This relation can be directly checked, focusing on a harmonic function of the brane solution in supergravity and implementing the T-duality [4] along the S1-direction that takes on isometry in the background geometry of the H-monopole [5,6,7,8]. The discussion above is based on supergravity theories that are low-energy effective theories of string theory, i.e. based on a point-particle picture in the limit that decouples massive modes in the string spectrum
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