Jeff Murugan

The emergent universe: an explicit construction

We provide a realization of a singularity-free inflationary universe in the form of a simple cosmological model dominated at early times by a single minimally coupled scalar field with a physically based potential. The universe starts asymptotically from an initial Einstein static state, which may be large enough to avoid the quantum gravity regime. It enters an expanding phase that leads to inflation followed by reheating and a standard hot big bang evolution. We discuss the basic characteristics of this emergent model and show that none is at odds with current observations.

On the trace-free Einstein equations as a viable alternative to general relativity

The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einsteins Field Equations by their trace-free part (the Trace-Free Einstein Equations), together with an independent assumption of energy--momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. However, one has to check that, as well as preserving the standard cosmological equations, this does not destroy other predictions, such as the junction conditions that underlie the use of standard stellar models. We confirm that no problems arise here: hence, the Trace-Free Einstein Equations are indeed viable for cosmological and astrophysical applications.

Particle-vortex duality in topological insulators and superconductors

A bstractWe investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path integral in the standard way, while in three dimensions, it takes the form of “self-duality in odd dimensions”. In this sense, it is closely related to the particle-vortex duality of planar systems. In particular, we use this to elaborate on Son’s conjecture that a three dimensional Dirac fermion that can be thought of as the surface mode of a four dimensional topological insulator is dual to a composite fermion.

More on Supersymmetric and 2d Analogs of the SYK Model

A bstractIn this paper, we explore supersymmetric and 2d analogs of the SYK model. We begin by working out a basis of (super)conformal eigenfunctions appropriate for expanding a four-point function. We use this to clarify some details of the 1d supersymmetric SYK model. We then introduce new bosonic and supersymmetric analogs of SYK in two dimensions. These theories consist of N fields interacting with random q-field interactions. Although models built entirely from bosons appear to be problematic, we find a supersymmetric model that flows to a large N CFT with interaction strength of order one. We derive an integral formula for the four-point function at order 1/N , and use it to compute the central charge, chaos exponent and some anomalous dimensions. We describe a problem that arises if one tries to find a 2d SYK-like CFT with a continuous global symmetry.

Non-Abelian BIonic Brane Intersections

withm > 2, it turns out that the matrix algebras contain more representations than is neededto describe functions on the sphere. In fact, in the classical limit (limit of large matrices),the matrix algebras related to even dimensional fuzzy spheres approach the algebra offunctions of the higher dimensional space SO(2k + 1)/U(k). It has been argued that theappearance of these extra dimensions is a consequence of the Myers effect[8].In thisarticlewestudy ”fuzzy funnel” solutionstothe non-Abelianequationsof motionof the D-string. Our funnel describes

A note on dual giant gravitons in AdS4 × ℂℙ3

We study some of the properties of dual giant gravitons - D2-branes wrapped on an S2⊂AdS4 - in type IIA string theory on AdS4×CP3. In particular we confirm that the spectrum of small fluctuations about the giant is both real and independent of the size of the graviton. We also extend previously developed techniques for attaching open strings to giants to this D2-brane giant and focus on two particular limits of the resulting string sigma model: In the pp-wave limit we quantize the string and compute the spectrum of bosonic excitations while in the semiclassical limit, we read off the fast string Polyakov action and comment on the comparison to the Landau-Lifshitz action for the dual open spin chain.

Classical and quantum integrability in AdS 2 / CFT 1

A bstractWe investigate the type IIA string on AdS2 × S2 × T6 supported by RR-flux which describes the gravitational side of the AdS2/CFT1 correspondence. While the four-dimensional part AdS2 × S2 can be realized as a supercoset, the full superstring has both coset and non-coset excitations, the latter giving rise to massless worldsheet modes, a somewhat novel feature in AdS/CFT. The string is nevertheless known to be integrable at the classical level. In this paper we perform several computations checking aspects of both classical and quantum string integrability. At the classical level we compute energies for the near BMN string and successfully match these against Bethe ansatz predictions. Furthermore, integrability dictates a magnon dispersion relation which we compare with the poles of loop corrected propagators, at both the one and two-loop level. At one loop, where only tadpole diagrams contribute, we find that the bosonic and fermionic contributions sum up to zero. Under the assumption of worldsheet supersymmetry, we then compute the two-loop sunset diagram in the near flat space limit. As in AdS5 × S5 we find that the result fits nicely into the sine-square structure of the dispersion relation.

Giant gravitons on deformed pp-waves

The recently constructed Lunin-Maldacena deformation of AdS5 × S5 is known to support two inequivalent Penrose limits that lead to BPS pp-wave geometries. In this note, we construct new giant graviton solutions on these backgrounds. A detailed study of the spectra of small fluctuations about these solutions reveals a remarkably rich structure. In particular, the giants that we contruct fall into two classes, one of which appears to remain stable in the Penrose limit independently of the strength of the deformation. The other class of giants, while more difficult to treat analytically, seems to exhibit a shape deformation not unlike the so- called ``squashed giants seen in the pp-wave with a constant NS B-field turned on. Some consideration is also given to the associated giant operators in the BMN limit of the dual = 1 SYM gauge theory.

Scattering in AdS 2 /CFT 1 and the BES phase

A bstractWe study worldsheet scattering for the type IIA superstring in AdS2 ×S2 ×T6. Using the Green-Schwarz action to quartic order in fermions we take the near-BMN limit, where as in the AdS3/CFT2 case there are both massive and massless excitations. For the massive excitations we compute all possible tree-level processes, and show that these agree with a truncated version of the exact AdS5 × S5 S-matrix. We also compute several S-matrix elements involving massless excitations. At one loop we find that the dressing phase is the same Hernándes-López phase appearing in AdS5/CFT4. We see the same phase when calculating this by semiclassical means using the PSU(1, 1|2)/U(1)2 coset sigma model, for which we can also study the scattering of fermions. This supports the conjecture that the all-loop dressing phase is again the BES phase, rather than a new phase like that seen in AdS3/CFT2.

Holonomy in the Schwarzschild-Droste geometry

Parallel transport of vectors in curved spacetimes generally results in a deficit angle between the directions of the initial and final vectors. We examine such a holonomy in the Schwarzschild-Droste geometry and find a number of interesting features that are not widely known. For example, parallel transport around circular orbits results in a quantized band structure of holonomy invariance. We also examine radial holonomy and extend the analysis to spinors and to the Reissner-Nordstrom metric, where we find qualitatively different behaviour for the extremal (Q = M) case. Our calculations provide a toolbox that will hopefully be useful in the investigation of quantum parallel transport in Hilbert-fibred spacetimes.