Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of type-IIB string theory and F-theory compactifications on Calabi-Yau fourfolds. In each case, the hierarchy of scales is fixed by a choice of Ramond-Ramond and Neveu-Schwarz fluxes in the compact manifold. Our solutions involve compactifications of the Klebanov-Strassler gravity dual to a confining $\mathcal{N}=1$ supersymmetric gauge theory, and the hierarchy reflects the small scale of chiral symmetry breaking in the dual gauge theory.

Hierarchies from fluxes in string compactifications

This is an extended version of our short report [1], where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results: We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS3/CFT2 case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS5 result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.

https://iopscience.iop.org/article/10.1088/1126-6708/2006/08/045/pdf

Aspects of Holographic Entanglement Entropy

We review the formalism of holographic renormalization. We start by discussing mathematical results on asymptotically anti-de Sitter (AdS) spacetimes. We then outline the general method of holographic renormalization. The method is illustrated by working all details in a simple example: a massive scalar field on anti-de Sitter spacetime. The discussion includes the derivation of the on-shell renormalized action, holographic Ward identities, anomalies and renormalization group (RG) equations, and the computation of renormalized one-, two- and four-point functions. We then discuss the application of the method to holographic RG flows. We also show that the results of the near-boundary analysis of asymptotically AdS spacetimes can be analytically continued to apply to asymptotically de Sitter spacetimes. In particular, it is shown that the Brown–York stress energy tensor of de Sitter spacetime is equal, up to a dimension-dependent sign, to the Brown–York stress energy tensor of an associated AdS spacetime.

https://iopscience.iop.org/article/10.1088/0264-9381/19/22/306/pdf

Lecture notes on holographic renormalization

http://cds.cern.ch/record/389927/files/9906070.pdf

CFT's from Calabi–Yau four-folds

We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well known difficulty of brane?antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation models can only work if restrictive assumptions about the method of volume stabilization, the warping of the internal space, and the source of inflationary energy are satisfied. We argue that this may not be a real problem, given the large range of available fluxes and background geometries in string theory.

Towards inflation in string theory

We revisit the singular IIB supergravity solution describing M fractional 3-branes on the conifold [hep-th/0002159]. Its 5-form flux decreases, which we explain by showing that the relevant \NN=1 SUSY SU(N+M)xSU(N) gauge theory undergoes repeated Seiberg-duality transformations in which N -> N-M. Far in the IR the gauge theory confines; its chiral symmetry breaking removes the singularity of hep-th/0002159 by deforming the conifold. We propose a non-singular pure-supergravity background dual to the field theory on all scales, with small curvature everywhere if the `t Hooft coupling g_s M is large. In the UV it approaches that of hep-th/0002159, incorporating the logarithmic flow of couplings. In the IR the deformation of the conifold gives a geometrical realization of chiral symmetry breaking and confinement. We suggest that pure \NN=1 Yang-Mills may be dual to strings propagating at small g_s M on a warped deformed conifold. We note also that the standard model itself may lie at the base of a duality cascade.

Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities

We present an identity relating the partition function of N = 4 supersymmetric QED to that of its dual under mirror symmetry. The identity is a generalized Fourier transform. Many known properties of abelian theories can be derived from this formula, including the mirror transforms for more general gauge and matter content. We show that N = 3 Chern-Simons QED and N = 4 QED with BF-type couplings are conformal field theories with exactly marginal couplings. Mirror symmetry acts on these theories as strong-weak coupling duality. After identifying the mirror of the gauge coupling (sometimes called the "magnetic coupling") we construct a theory which is exactly mirror - at all scales - to N = 4 SQED. We also study vortex-creation operators in the large N-f limit.

/pdf/on-mirror-symmetry-in-three-dimensional-abelian-gauge-568cn3ogos.pdf

On Mirror Symmetry in Three Dimensional Abelian Gauge Theories

In supersymmetric models, W -inos, partners of the SU(2) gauge bosons, may be the lightest supersymmetric particles. For generic parameters, charged and neutral W -inos are highly degenerate. Charged W -inos travel macroscopic distances, but can decay to neutral W -inos and extremely soft leptons or pions before reaching the muon chambers, thereby circumventing conventional trigger requirements. However, these charginos are detectable, and can be triggered on when produced in association with jets. In addition, we propose a new trigger for events with a high p[sub T] track and low hadronic activity. For Tevatron RunthinspthinspII with luminosity 2 fb[sup [minus]1] , the proposed searches can discover W -inos with masses up to 300thinspthinspGeV and explore a substantial portion of the parameter space in sequestered sector models. [copyright] [ital 1999] [ital The American Physical Society ]

Discovering Supersymmetry at the Tevatron in W -ino Lightest Supersymmetric Particle Scenarios

Confinement and strings in MQCD

We present a new mechanism, which does not require any flavor symmetry, to explain the small Yukawa couplings and CKM mixing angles. The Yukawa matrices are assumed to be random at short distances and the hierarchical structure is generated in the infrared by renormalization group flow. The generic qualitative predictions of this mechanism are in good agreement with observation. We give several simple examples in supersymmetric theories. We show that our mechanism can also ameliorate the supersymmetric flavor problem, and make predictions for the superpartner mass spectrum. The mechanism is fully consistent with grand unification, and in SU(5)-based models of neutrino mass, predicts a large mixing angle for νμ↔ντ oscillations.

Matthew J. Strassler

Papers

Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities

On Mirror Symmetry in Three Dimensional Abelian Gauge Theories

Discovering Supersymmetry at the Tevatron in W -ino Lightest Supersymmetric Particle Scenarios

Confinement and strings in MQCD

Suppressing flavor anarchy