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Abstract:The question of what happens when the heterotic SO(32) instanton becomes small was answered sometime back by Witten. The heterotic theory develops an enhanced Sp(2k) gauge symmetry for k small instantons, besides the allowed SO(32) gauge symmetry. An interesting question now is to ask what happens when we take the large k limit. In this paper we argue that in some special cases, where Gauss' law allows the large k limit, the dynamics of the large k small instantons can be captured by a dual gravitational description. For the cases that we elaborate in this paper, the gravity duals are non-Kähler manifolds although in general they could be non-geometric. These small instantons are heterotic five-branes and the duality allows us to study the strongly coupled field theories on these five-branes. We review and elaborate on some of the recent observations pointing towards this duality, and argue that in certain cases the gauge/gravity duality may be understood as small instanton transitions under which the instantons smoothen out and consequently lose the Sp(2k) gauge symmetry. This may explain how branes disappear on the dual side and are replaced by fluxes. We analyse the torsion classes before and after the transitions, and discuss briefly how the ADHM sigma model and related vector bundles could be studied for these scenarios.

We propose a new realization of axion monodromy inflation in which axion monodromy arises from torsional cycles in a type IIB compactification. A class of monomial potentials is obtained with specific values for the power index. Moreover, the inflaton mass changes profile due to the couplings between various fields after compactification. Consequently, the potential obtains a step-like profile at some critical scale. We study the cosmological implications of one concrete realization of this model. At the background level, it realizes a sufficiently long inflationary stage, which allows for the violation of the slow-roll conditions for a short period of time when the inflaton is close to the critical scale. Accordingly, the Hubble horizon is perturbed and affects the dynamics of primordial cosmological perturbations. In particular, we analyze the angular power spectrum of B-mode polarization and find a boost on very large scales. We also find that the amplitude of scalar perturbations is suppressed near the critical scale. Thus our model provides an interpretation for the low-suppression of temperature anisotropies in the CMB power spectrum. We examine these effects and confront the model to observations.

Abstract:We study extremal two-charge fuzzball geometries, with attention to the use of the proper duality frame. For zero angular momentum there is an onion-like structure, and the smooth D1-D5 geometries are not valid for typical states. Rather, these geometries are best approximated by geometries with stringy sources, or by a free CFT. For nonzero angular momentum we find a regime where smooth fuzzball solutions are the correct description. Our analysis rests on the comparison of three radii: the typical fuzzball radius, the entropy radius determined by the microscopic theory, and the breakdown radius where the curvature becomes large. We attempt to draw more general lessons.

Gravity duals for little string theories -which give rise to four-dimensional theories that undergo permanent confinement in the infrared -have not been studied in great detail. We address this question in the framework of heterotic SO(32) and E 8 × E 8 string theory, constructing these backgrounds by wrapping heterotic five-branes on calibrated two-cycles of non-Kähler resolved conifolds. Related to deformations of the underlying little string theories, we find numerous analytic solutions preserving N = 1 supersymmetry in fourdimensions. These theories all have non-abelian global symmetries that generally arise from both the heterotic vector bundle and from certain orbifold states. In the decoupling limit, we argue that the gravity duals are given by non-Kähler manifolds that have both blown-up two-cycles and three-cycles at the origin. We argue this following certain duality sequences that include M-theory torsional manifolds at an intermediate step, which help us to construct new type I ′ gauge/gravity duality pairs. In the M-theory duality frame, we also elucidate new sequences of flips and flops.1 This can also be seen from a sigma model analysis of the background, see [10]. 2 For an early history and progress report on LSTs, see the excellent review [13]. 3 This is different from D-branes, which have local QFTs because the LSTs, being given by the NS5-branes, do not change dimension under longitudinal T-dualities. Since the worldvolume theories just shifts from one description to another, they don't have a well-defined energy-momentum tensor [12]. 4 The theories that we are most interested in are the LSTs compactified on a two-sphere, giving rise to four-dimensional theories below a certain energy scale. In this paper, we will be particularly interested in the confining behavior in the deep infrared, so the UV completion will be beyond the scope of our discussions.