119 research outputs found
Aspects of Higher Spin Theories Conformal Field Theories and Holography
No full textThis dissertation consist of three parts. The first part of the thesis is devoted to the study of gravity and higher spin gauge theories in 2+1 dimensions. We construct cosmological so-lutions of higher spin gravity in 2+1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary CFT partition function, and reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using a prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS3. For the case of negative cosmological constant we show that interpreting the inverse AdS3 radius 1=l as a Grassmann variable results in a formal map from gravity in AdS3 to gravity in flat space. The underlying reason for this is the fact that ISO(2,1) is the Inonu-Wigner contraction of SO(2,2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS3 case. Our results straightforwardly generalize to the higher spin case: the flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We also demonstrate the power of our approach by doing singularity resolution in the BMS gauge as an application. Finally, we construct a candidate for the most general chiral higher spin theory with AdS3 boundary conditions. In the Chern-Simons language, the left-moving solution has Drinfeld-Sokolov reduced form, but on the right-moving solution all charges and chemical potentials are turned on. Altogether (for the spin-3 case) these are 19 functions. Despite this, we show that the resulting metric has the form of the “most general” AdS3 boundary conditions discussed by Grumiller and Riegler. The asymptotic symmetry algebra is a product of a W3 algebra on the left and an affine sl(3)k current algebra on the right, as desired. The metric and higher spin fields depend on all the 19 functions.
The second part is devoted to the problem of Neumann boundary condition in Einstein’s gravity. The Gibbons-Hawking-York (GHY) boundary term makes the Dirichlet problem for gravity well defined, but no such general term seems to be known for Neumann boundary conditions. In our work, we view Neumann boundary condition not as fixing the normal derivative of the metric (“velocity”) at the boundary, but as fixing the functional derivative of the action with respect to the boundary metric (“momentum”). This leads directly to a new boundary term for gravity: the trace of the extrinsic curvature with a specific dimension-dependent coefficient. In three dimensions this boundary term reduces to a “one-half” GHY term noted in the literature previously, and we observe that our action translates precisely to the Chern-Simons action with no extra boundary terms. In four dimensions the boundary term vanishes, giving a natural Neumann interpretation to the standard Einstein-Hilbert action without boundary terms. We also argue that a natural boundary condition for gravity in asymptotically AdS spaces is to hold the renormalized boundary stress tensor density fixed, instead of the boundary metric. This leads to a well-defined variational problem, as well as new counter-terms and a finite on-shell action. We elaborate this in various (even and odd) dimensions in the language of holographic renormalization. Even though the form of the new renormalized action is distinct from the standard one, once the cut-off is taken to infinity, their values on classical solutions coincide when the trace anomaly vanishes. For AdS4, we compute the ADM form of this renormalized action and show in detail how the correct thermodynamics of Kerr-AdS black holes emerge. We comment on the possibility of a consistent quantization with our boundary conditions when the boundary is dynamical, and make a connection to the results of Compere and Marolf. The difference between our approach and microcanonical-like ensembles in standard AdS/CFT is emphasized.
In the third part of the dissertation, we use the recently developed CFT techniques of Rychkov and Tan to compute anomalous dimensions in the O(N) Gross-Neveu model in d = 2 + dimensions. To do this, we extend the “cow-pie contraction” algorithm of Basu and Krishnan to theories with fermions. Our results match perfectly with Feynman diagram computations
Contractions from grading
No full textWe note that large classes of contractions of algebras that arise in physics can be understood purely algebraically via identifying appropriate Z(m)-gradings (and their generalizations) on the parent algebra. This includes various types of flat space/Carroll limits of finite and infinite dimensional (A) dS algebras, as well as Galilean and Galilean conformal algebras. Our observations can be regarded as providing a natural context for the Grassmann approach of Krishnan et al. J. High Energy Phys. 2014(3), 36]. We also introduce a related notion, which we call partial grading, that arises naturally in this context. Published by AIP Publishing
Applications of Holography
No full textThis thesis consists of four parts. In the first part of the thesis, we investigate the phase
structure of Einstein-Maxwell-Scalar system with a negative cosmological constant. For
the conformally coupled scalar, an intricate phase diagram is charted out between the four
relevant solutions: global AdS, boson star, Reissner-Nordstrom black hole and the hairy
black hole. The nature of the phase diagram undergoes qualitative changes as the charge of
the scalar is changed, which we discuss. We also discuss the new features that arise in the
extremal limit.
In the second part, we do a systematic study of the phases of gravity coupled to an
electromagnetic field and charged scalar in flat space, with box boundary conditions. The
scalar-less box has previously been investigated by Braden, Brown, Whiting and York (and
others) before AdS/CFT and we elaborate and extend their results in a language more
familiar from holography. The phase diagram of the system is analogous to that of AdS
black holes, but we emphasize the differences and explain their origin. Once the scalar
is added, we show that the system admits both boson stars as well as hairy black holes as
solutions, providing yet another way to evade flat space no-hair theorems. Furthermore both
these solutions can exist as stable phases in regions of the phase diagram. The final picture of
the phases that emerges is strikingly similar to that of holographic superconductors in global
AdS, discussed in part one. We also point out previously unnoticed subtleties associated to
the definition quasi-local charges for gravitating scalar fields in finite regions.
In part three, we investigate a class of tensor models which were recently outlined as potentially
calculable examples of holography, as their perturbative large-N behavior is similar
to the Sachdev-Ye-Kitaev (SYK) model, but they are fully quantum mechanical (in the sense
that there is no quenched disorder averaging). We explicitly diagonalize the simplest nontrivial
Gurau-Witten tensor model and study its spectral and late-time properties. We find
parallels to (a single sample of) SYK where some of these features were recently attributed
to random matrix behavior and quantum chaos. In particular, after a running time average,
the spectral form factor exhibits striking qualitative similarities to SYK. But we also observe
that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy
of intermediate energy states, not seen in SYK. If one ignores the delta function due to the
degeneracies however, there is level repulsion in the unfolded spacing distribution hinting
chaos. Furthermore, the spectrum has gaps and is not (linearly) rigid. The system also has
a spectral mirror symmetry which we trace back to the presence of a unitary operator with
which the Hamiltonian anticommutes. We use it to argue that to the extent that the model
exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the
BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.
In part four, we construct general asymptotically Klebanov-Strassler solutions of a five
dimensional SU(2) SU(2) Z2 Z2R truncation of IIB supergravity on T1;1, that break
supersymmetry. This generalizes results in the literature for the SU(2) SU(2) Z2 U(1)R
case, to a truncation that is general enough to capture the deformation of the conifold in
the IR. We observe that there are only two SUSY-breaking modes even in this generalized
set up, and by holographically computing Ward identities, we confirm that only one of them
corresponds to spontaneous breaking: this is the mode triggered by smeared anti-D3 branes
at the tip of the warped throat. Along the way, we address some aspects of the holographic
computation of one-point functions of marginal and relevant operators in the cascading gauge
theory. Our results strengthen the evidence that if the KKLT construction is meta-stable, it
is indeed a spontaneously SUSY-broken (and therefore bona fide) vacuum of string theory
Aspects of Holography and Quantum complexity
No full textWe begin with the Principle of holography and the AdS/CFT correspondence. We begin our investigations by considering the Principle of Holography, at the level of codimension-1 screens. We argue that the mechanism of encoding the holographic data in terms of sources, condensates, and correlators is fairly general and has generalizations to a large class of spacetimes. We formulate the holographic correspondence in terms of bulk sources localized on a screen, instead of boundary values of bulk fields. We discuss the extension of the familiar notion of normalizable and non-normalizable modes to moderately general settings beyond AdS. We discuss a simple map between this prescription and the usual AdS/CFT correspondence, as well as work out explicit correlators via this prescription in flat space. Finally, we discuss the general utility of this approach of using sources to describe dynamics.
We then focus on the widely successful AdS/CFT correspondence. Specifically, we study the Bulk Reconstruction program in AdS/CFT. We discuss various aspects of the HKLL bulk reconstruction in AdS. We construct the space-like Kernel for the non-normalizable mode as a mode sum and via a Green's function approach (in even dimensions). This puts the normalizable and non-normalizable modes on equal footing. In Poincaré AdS, we delve into the technical details of this construction. We propose a spatial complexification and discuss an antipodal identification as crucial steps in obtaining a space-like Kernel in terms of the chordal distance, for certain values of scaling dimension. We also note some interesting features of this construction inside the Brietienlohner-Freedman bound, where both the normalizable and non-normalizable modes have equivalent interpretations.
At this stage, we shift gears and start addressing some problems in quantum chaos via quantum complexity. In view of the Operator Growth Hypothesis for chaotic and intergable systems, we study classically integrable systems with unstable saddle points. We find that Krylov complexity (of operators) is a hypersensitive probe of chaos. We discuss some features of Krylov complexity and autocorrelation functions. We supplement our study by numerical calculations using the Lipkin-Meshkov-Glick and Feigngold-Peres models.
Using Krylov complexity, we also study quantum many-body scars. We utilize the Lanczos mechanism to study special eigenstates for the (chaotic) PXP model which behave as states with ``low chaos'' as compared to the other eigenstates. The presence of these states indicate the emergence of some underlying symmetry, which we characterize by deformed SU(2) algebra. Finally, we study the nature Krylov spread complexity for the scar states and compare them to the generic states. We conclude by discussing a ``tight-binding'' interpretation of Krylov spread complexity
Exact Solution of a Strongly Coupled Gauge Theory in 0+1 Dimensions
No full textGauged tensor models are a class of strongly coupled quantum mechanical theories. We present the exact analytic solution of a specific example of such a theory: namely, the smallest colored tensor model due to Gurau and Witten that exhibits nonlinearities. We find explicit analytic expressions for the eigenvalues and eigenstates, and the former agree precisely with previous numerical results on (a subset of) eigenvalues of the ungauged theory. The physics of the spectrum, despite the smallness of N, exhibits rudimentary signatures of chaos. This Letter is a summary of our main results: the technical details will appear in companion paper C. Krishnan and K. V. Pavan Kumar, Complete solution of a gauged tensor model, arXiv:1804.10103]
A New Gauge for Asymptotically Flat Spacetime
No full textWe present a new gauge for asymptotically flat spacetime that can treat
future and past null infinities ( or )
democratically. Our gauge is complementary to Bondi and Ashtekar-Hansen gauges,
and is adapted to the -matrix being the natural observable. One new feature
is that the holographic directions are null. We present a set of consistent
fall-offs in terms of null coordinates at and
, with finite BMS charges. The diagonal BMS
symmetry of the gravitational -matrix emerges upon demanding {\em
asymptotic} CPT invariance. Trivial diffeomorphisms, (absence of) log
fall-offs, possible enhancements of BMS algebra, and the possibility of
holographic renormalization of data at and
, play interesting roles. Gory details of the various new
technical features that emerge, are elaborated in a companion paper to this
letter.Comment: 5 pages. v2,v3: typos fixed, slight re-wording, refs added, v4:
clarifications, speculative comments, author emails and references adde
Quantum Critical Superfluid Flows and Anisotropic Domain Walls
No full textWe construct charged anisotropic AdS domain walls as solutions of a consistent truncation of type IIB string theory. These are a one-parameter family of solutions that flow to an AdS fixed point in the IR, exhibiting emergent conformal invariance and quantum criticality. They represent the zero-temperature limit of the holographic superfluids at finite superfluid velocity constructed in arXiv:1010.5777. We show that these domain walls exist only for velocities less than a critical value, agreeing in detail with a conjecture made there. We also comment about the IR limits of flows with velocities higher than this critical value, and point out an intriguing similarity between the phase diagrams of holographic superfluid flows and those of ordinary superconductors with imbalanced chemical potential
Type IIB holographic superfluid flows
No full textWe construct fully backreacted holographic superfluid flow solutions in a five-dimensional theory that arises as a consistent truncation of low energy type IIB string theory. We construct a black hole with scalar and vector hair in this theory, and study the phase diagram. As expected, the superfluid phase ceases to exist for high enough superfluid velocity, but we show that the phase transition between normal and superfluid phases is always second order. We also analyze the zero temperature limit of these solutions. Interestingly, we find evidence that the emergent IR conformal symmetry of the zero-temperature domain wall is broken at high enough velocity
Can quantum de Sitter space have finite entropy?
No full textIf one tries to view de Sitter as a true (as opposed to a meta-stable) vacuum, there is a tension between the finiteness of its entropy and the infinite dimensionality of its Hilbert space. We investigate the viability of one proposal to reconcile this tension using q-deformation. After defining a differential geometry on the quantum de Sitter space, we try to constrain the value of the deformation parameter by imposing the condition that in the undeformed limit, we want the real form of the (inherently complex) quantum group to reduce to the usual SO(4, 1) of de Sitter. We find that this forces q to be a real number. Since it is known that quantum groups have finite-dimensional representations only for q≤ root of unity, this suggests that standard q-deformations cannot give rise to finite-dimensional Hilbert spaces, ruling out finite entropy for q-deformed de Sitter. © 2007 IOP Publishing Ltd.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
AdS 4/CFT 3 at one loop
No full textI consider semi-classical type IIA strings rotating in the AdS 4 part of AdS 4 × ℂℙ 3. The one loop sigma model corrections to this classical solution are used to compute the energy shift, and the result is found to be E-S = f(λ)ln S with f(λ) = (√2λ) 1/2-(5ln 2/2π)+(1/√λ) 1/2). Even though the functional forms match, the actual numerical value of this one loop string result differs from the result obtained on the integrable N = 6 Chern-Simons (ABJM) theory side. © 2008 SISSA.SCOPUS: ar.jinfo:eu-repo/semantics/publishe
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