Stable non-supersymmetric throats in string theory

Abstract

We construct a large class of non-supersymmetric AdS-like throat geometries in string theory by taking non-supersymmetric orbifolds of supersymmetric backgrounds. The scale of SUSY breaking is the AdS radius, and the dual field theory has explicitly broken supersymmetry. The large hierarchy of energy scales in these geometries is stable. We establish this by showing that the dual gauge theories do not have any relevant operators which are singlets under the global symmetries. When the geometries are embedded in a compact internal space, a large enough discrete subgroup of the global symmetries can still survive to prevent any singlet relevant operators from arising. We illustrate this by embedding one case in a non-supersymmetric orbifold of a Calabi-Yau manifold. These examples can serve as a starting point for obtaining Randall-Sundrum models in string theory, and more generally for constructing composite Higgs or technicolor-like models where strongly coupled dynamics leads to the breaking of electro-weak symmetry. Towards the end of the paper, we briefly discuss how bulk gauge fields can be incorporated by introducing D7-branes in the bulk, and also show how the strongly coupled dynamics can lead to an emergent weakly coupled gauge theory in the IR with matter fields including scalars.

Randall-Sundrum and strings

“…Any real string construction of RS would also face a number of challenges we haven't discussed, including understanding stability of non-supersymmetric backgrounds and avoiding singlet relevant operators that would prevent the theory from solving the hierarchy problem [15,16]. Our bounds suggest that these problems must be solved in a regime where α corrections are important, if they are to yield phenomenologically viable solutions.…”

“…This instability is similar to the original "bubble of nothing" instability of the Kaluza-Klein vacuum, arising from solutions in which the circle fiber shrinks to zero size at the edge of a bubble [44]. Despite this instability, similar orbifolds have been discussed as a source of stable non-supersymmetric RS-like spaces in string theory, because if such a throat is embedded in a Calabi-Yau, the lifetime of the space can be longer than the age of our universe [16]. However, the decay width goes as Γ ∼ k 9 Λ 4 UV exp − N 2 k 8 , so that if we approach the limit k ∼ N 1/4 , the entire space would very rapidly decay.…”

“…The main focus of this paper will be providing details of these two arguments, and investigating possible ranges of the ratio m str /m KK . We focus on various stringy implementation of this type of model, setting aside orthogonal issues that make stringy UV completion of nonsupersymmetric RS a challenge [15,16].…”

Inflation and String Theory

“…The DBI mechanism, which turns a steep potential from a liability into an asset, will be discussed in §5.3. Discrete symmetries can be used to forbid problematic mass terms [652], and in some cases have been shown to be compatible with moduli stabilization [657]. Dynamical mechanisms have also been found: it was shown in [653,655] that if N D3-branes become trapped in a metastable 13 The restriction to irrelevant perturbations in [553] rests on the requirement that the background throat solution is a good approximation in the infrared.…”

Moduli stabilization and the holographic RG for AdS and dS

“…in the study of AdS/CFT and warped compactifications: freely-acting supersymmetrybreaking orbifold theories [23][24][25] are only perturbatively stable. When we impose a cutoff by embedding them in a warped compactification, these theories are metastable; they survive for exponentially long (as a function of large inverse couplings) but ultimately decay.…”