arXiv subjects

Albion Lawrence

Publications and source records attributed to Albion Lawrence.

At least 37 records · Page 2Linked to original sources

arXiv2015

Large Field Inflation and Gravitational Entropy

Large field inflation can be sensitive to perturbative and nonperturbative quantum corrections that spoil slow roll. A large number $N$ of light species in the theory, which occur in many string constructions, can amplify these problems. One might even worry that in a de Sitter background, light species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem when we correctly renormalize models with many light species, taking the {\it physical} Planck scale to be $M^2_{pl} \gtrsim N {\cal M}_{UV}^2$, where ${\cal M}_{UV}$ is the cutoff for the QFT coupled to semiclassical quantum gravity. The number of light species then cancels out of the gravitational entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong coupling scale for the axion dynamics, we show that it is {\it not} in general the cutoff of 4d semiclassical gravity. After renormalizing the two point function of the inflaton, we note that it is also controlled by scales much below the cutoff. We revisit $N$-flation and KKLT-type compactifications in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it.

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arXiv2014

Causality & holographic entanglement entropy

We identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.

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arXiv2014

Metastability and instability in holographic gauge theories

We review and extend previous results regarding the stability and thermodynamics of Anti-de Sitter (AdS) spacetime at finite temperature. Using a combination of analytic and numerical techniques, we compute the energy, temperature, and entropy of perfect fluid stars in asymptotically AdS spacetimes. We find that at sufficiently high temperature (in the canonical ensemble) or energy (in the microcanonical ensemble) these configurations develop dynamical instabilities, which presumably lead to the formation of a black hole. We extend our analysis to the case of $AdS \times S$ compactifications stabilized by flux (such as those that arise in supergravity and string theory), and find that the inclusion of the sphere does not substantially alter these results. We then map out the phase structure of these theories in the canonical and microcanonical ensembles, paying attention to inequivalence of these ensembles for global anti-de Sitter space. With a certain scaling limit, the critical temperature can be parametrically lower than the string temperature, so that supergravity is a good description at the instability point. We comment on the implications of this for the unitarity of black holes.

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arXiv2014

Natural Chaotic Inflation and UV Sensitivity

If the recent measurement of B-mode polarization by BICEP2 is due to primordial gravitational waves, it implies that inflation was driven by energy densities at the GUT scale $M_{GUT} \sim 2\times 10^{16} GeV$. This favors single-field chaotic inflation models. These models require transplanckian excursions of the inflaton, forcing one to address the UV completion of the theory. We use a benchmark 4d effective field theory of axion-4-form inflation to argue that inflation driven by a quadratic potential (with small corrections) is well motivated in the context of high-scale string theory models; that it presents an interesting incitement for string model building; and the dynamics of the UV completion can have observable consequences.

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arXiv2013

Bose-Fermi duality and entanglement entropies

Entanglement (Renyi) entropies of spatial regions are a useful tool for characterizing the ground states of quantum field theories. In this paper we investigate the extent to which these are universal quantities for a given theory, and to which they distinguish different theories, by comparing the entanglement spectra of the massless Dirac fermion and the compact free boson in two dimensions. We show that the calculation of Renyi entropies via the replica trick for any orbifold theory includes a sum over orbifold twists on all cycles. In a modular-invariant theory of fermions, this amounts to a sum over spin structures. The result is that the Renyi entropies respect the standard Bose-Fermi duality. Next, we investigate the entanglement spectrum for the Dirac fermion without a sum over spin structures, and for the compact boson at the self-dual radius. These are not equivalent theories; nonetheless, we find that (1) their second Renyi entropies agree for any number of intervals, (2) their full entanglement spectra agree for two intervals, and (3) the spectrum generically disagrees otherwise. These results follow from the equality of the partition functions of the two theories on any Riemann surface with imaginary period matrix. We also exhibit a map between the operators of the theories that preserves scaling dimensions (but not spins), as well as OPEs and correlators of operators placed on the real line. All of these coincidences can be traced to the fact that the momentum lattice for the bosonized fermion is related to that of the self-dual boson by a 45 degree rotation that mixes left- and right-movers.

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arXiv2012

Holographic interpretations of the renormalization group

In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the bulk fields fluctuate. Recent work has used a Wilsonian framework to propose an alternative identification of the running couplings in terms of non-fluctuating data; in the classical limit, these new couplings do not satisfy the bulk equations of motion. We study renormalization scheme dependence in the latter formalism, and show that a scheme exists in which couplings to single trace operators realize particular solutions to the bulk equations of motion, in the semiclassical limit. This occurs for operators with dimension $Δ\notin \frac{d}{2} + \ZZ$, for sufficiently low momenta. We then clarify the relation between the saddle point approximation to the Wilsonian effective action ($S_W$) and boundary conditions at a cutoff surface in AdS space. In particular, we interpret non-local multi-trace operators in $S_W$ as arising in Lorentzian AdS space from the temporary passage of excitations through the UV region that has been integrated out. Coarse-graining these operators makes the action effectively local.

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arXiv2012

θ-angle monodromy in two dimensions

"θ-angle monodromy" occurs when a theory possesses a landscape of metastable vacua which reshuffle as one shifts a periodic coupling θby a single period. "Axion monodromy" models arise when this parameter is promoted to a dynamical pseudoscalar field. This paper studies the phenomenon in two-dimensional gauge theories which possess a U(1) factor at low energies: the massive Schwinger and gauged massive Thirring models, the U(N) 't Hooft model, and the {\mathbb CP}^N model. In all of these models, the energy dependence of a given metastable false vacuum deviates significantly from quadratic dependence on θjust as the branch becomes completely unstable (distinct from some four-dimensional axion monodromy models). In the Schwinger, Thirring, and 't Hooft models, the meson masses decrease as a function of θ. In the U(N) models, the landscape is enriched by sectors with nonabelian θterms. In the {\mathbb CP}^N model, we compute the effective action and the size of the mass gap is computed along a metastable branch.

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arXiv2011

Axion monodromy in a model of holographic gluodynamics

The low energy field theory for N type IIA D4-branes at strong 't Hooft coupling, wrapped on a circle with antiperiodic boundary conditions for fermions, is known to have a vacuum energy which depends on the $θ$ angle for the gauge fields, and which is a multivalued function of this angle. This gives a field-theoretic realization of "axion monodromy" for a nondynamical axion. We construct the supergravity solution dual to the field theory in the metastable state which is the adiabatic continuation of the vacuum to large values of $θ$. We compute the energy of this state and show that it initially rises quadratically and then flattens out. We show that the glueball mass decreases with $θ$, becoming much lower than the 5d KK scale governing the UV completion of this model. We construct two different classes of domain walls interpolating between adjacent vacua. We identify a number of instability modes -- nucleation of domain walls, bulk Casimir forces, and condensation of tachyonic winding modes in the bulk -- which indicate that the metastable branch eventually becomes unstable. Finally, we discuss two phenomena which can arise when the axion is dynamical; axion-driven inflation, and axion strings.

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arXiv2010

An Ignoble Approach to Large Field Inflation

We study an inflationary model developed by Kaloper and Sorbo, in which the inflaton is an axion with a sub-Planckian decay constant, whose potential is generated by mixing with a topological 4-form field strength. This gives a 4d construction of "axion monodromy inflation": the axion winds many times over the course of inflation and draws energy from the 4-form. The classical theory is equivalent to chaotic inflation with a quadratic inflaton potential. Such models can produce "high scale" inflation driven by energy densities of the order of $(10^{16}\ GeV)^4$, which produces primordial gravitational waves potentially accessible to CMB polarization experiments. We analyze the possible corrections to this scenario from the standpoint of 4d effective field theory, identifying the physics which potentially suppresses dangerous corrections to the slow-roll potential. This yields a constraint relation between the axion decay constant, the inflaton mass, and the 4-form charge. We show how these models can evade the fundamental constraints which typically make high-scale inflation difficult to realize. Specifically, the moduli coupling to the axion-four-form sector must have masses higher than the inflationary Hubble scale ($\la\ 10^{14}\ GeV$). There are also constraints from states that become light due to multiple windings of the axion, as happens in explicit string theory constructions of this scenario. Further, such models generally have a quantum-mechanical "tunneling mode" in which the axion jumps between windings, which must be suppressed. Finally, we outline possible observational signatures.

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arXiv2009

Exact null tachyons from RG flows

We construct exact 2d CFTs, corresponding to closed string tachyon and metric profiles invariant under shifts in a null coordinate, which can be constructed from any 2d renormalization group flow. These solutions satisfy first order equations of motion in the conjugate null coordinate. The direction along which the tachyon varies is identified precisely with the worldsheet scale, and the tachyon equations of motion are the RG flow equations.

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arXiv2009

Insightful D-branes

We study a simple model of a black hole in AdS and obtain a holographic description of the region inside the horizon. A key role is played by the dynamics of the scalar fields in the dual gauge theory. This leads to a proposal for a dual description of D-branes falling through the horizon of any AdS black hole. The proposal uses a field-dependent time reparameterization in the field theory. We relate this reparametrization to various gauge invariances of the theory. Finally, we speculate on information loss and the black hole singularity in this context.

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arXiv2008

F-term SUSY Breaking and Moduli

We discuss the coupling of heavy moduli fields to light fields when the dynamics of the latter, absent such couplings, yields metastable vacua. We show that the survival of the vacuum structure of the local model depends nontrivially on the cross-couplings of the two sectors. In particular we find that for "local" models (such as those realized by D-branes in type II string theories) with metastable vacua breaking supersymmetry via F-terms, cross-coupling of the two sectors at an intermediate scale can push the metastable vacuum outside of the regime of the effective field theory. We parametrize the region in which the metastable vacua are safe. We the show that sufficiently small cross-couplings can be made natural. Finally, we briefly discuss the role of moduli in stringy realizations of "retrofitted" SUSY-breaking sectors.

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arXiv2008

Torsion and Supersymmetry Breaking

We identify the auxiliary fields in the hypermultiplets of type IIB string theory compactified on a Calabi-Yau manifold, using a combination of worldsheet and supergravity techniques. The SUSY-breaking squark and gaugino masses in type IIB models depend on these auxiliary fields, which parametrize deformations away from a pure Calabi-Yau compactification to one with NS-NS 3-form flux and SU(3) x SU(3) structure. Worldsheet arguments show that such compactifications are generically globally nongeometric. Our results, combined with earlier results for type IIA compactifications, imply that these deformations are the mirrors of NS-NS 3-form flux, in accord with work from the supergravity point of view. Using the worldsheet current algebra, we explain why mirror symmetry may continue to hold in the presence of fluxes breaking the symmetries (e.g., (2,2) SUSY) on which mirror symmetry is typically taken to depend. Finally, we give evidence that nonperturbative worldsheet effects (such as worldsheet instantons) provide important corrections to the supergravity picture in the presence of auxiliary fields for Kahler moduli.

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arXiv2007

Scattering of twist fields from D-branes and orientifolds

We compute the two-point function for Z_N orbifold twist fields on the disk and RP2. We apply this to a computation of the O(g_s) correction to the Kahler potential for (the symmetric combination of) blow-up modes in type I string theory on T^6/Z_3. This is related by supersymmetry to the one-loop field dependent correction to the Fayet-Iliopoulos D-term for the anomalous U(1) factor. We find this correction to be non-vanishing away from the orbifold point.

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arXiv2007

Dimensional Duality

We show that string theory on a compact negatively curved manifold, preserving a U(1)^{b_1} winding symmetry, grows at least b_1 new effective dimensions as the space shrinks. The winding currents yield a "D-dual" description of a Riemann surface of genus h in terms of its 2h dimensional Jacobian torus, perturbed by a closed string tachyon arising as a potential energy term in the worldsheet sigma model. D-branes on such negatively curved manifolds also reveal this structure, with a classical moduli space consisting of a b_1-torus. In particular, we present an AdS/CFT system which offers a non-perturbative formulation of such supercritical backgrounds. Finally, we discuss generalizations of this new string duality.

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arXiv2007

Bulk perturbations of N=2 branes

The evolution of supersymmetric A-type D-branes under the bulk renormalization group flow between two different N=2 minimal models is studied. Using the Landau-Ginzburg description we show that a specific set of branes decouples from the infrared theory, and we make detailed predictions for the behavior of the remaining branes. The Landau-Ginzburg picture is then checked against a direct conformal field theory analysis. In particular we construct a natural index pairing which is preserved by the RG flow, and show that the branes that decouple have vanishing index with the surviving branes.

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arXiv2006

Holography and Renormalization in Lorentzian Signature

De Boer et. al. have found an asymptotic equivalence between the Hamilton-Jacobi equations for supergravity in (d+1)-dimensional asymptotic anti-de Sitter space, and the Callan-Symanzik equations for the dual d-dimensional perturbed conformal field theory. We discuss this correspondence in Lorentzian signature. We construct a gravitational dual of the generating function of correlation functions between initial and final states, in accordance with the construction of Marolf, and find a class of states for which the result has a classical supergravity limit. We show how the data specifying the full set of solutions to the second-order supergravity equations of motion are described in the field theory, despite the first-order nature of the renormalization group equations for the running couplings: one must specify both the couplings and the states, and the latter affects the solutions to the Callan-Symanzik equations.

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arXiv2006

Random walks and the Hagedorn transition

We study details of the approach to the Hagedorn temperature in string theory in various static spacetime backgrounds. We show that the partition function for a {\it single} string at finite temperature is the torus amplitude restricted to unit winding around Euclidean time. We use the worldsheet path integral to derive the statement that the the sum over random walks of the thermal scalar near the Hagedorn transition is precisely the image under a modular transformation of the sum over spatial configurations of a single highly excited string. We compute the radius of gyration of thermally excited strings in $AdS_D\times S^n$. We show that the winding mode indicates an instability despite the AdS curvature at large radius, and that the negative mass squared decreases with decreasing AdS radius, much like the type 0 tachyon. We add further arguments to statements by Barbon and Rabinovici, and by Adams {\it et. al.}, that the Euclidean AdS black hole can thought of as a condensate of the thermal scalar. We use this to provide circumstantial evidence that the condensation of the thermal scalar decouples closed string modes.

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