The High Energy Behavior of Mellin Amplitudes

In any consistent massive quantum field theory there are well-known bounds on scattering amplitudes at high energies. In conformal field theory there is no scattering amplitude, but the Mellin amplitude is a well-defined object analogous to the scattering amplitude. We prove bounds at high energies on Mellin amplitudes in conformal field theories, valid under certain technical assumptions. Such bounds are derived by demanding the absence of spurious singularities in position space correlators. We also conjecture a stronger bound, based on evidence from several explicit examples

Gravitational orbits, double-twist mirage, and many-body scars

We explore the implications of stable gravitational orbits around an AdS black hole for the boundary conformal field theory. The orbits are long-lived states that eventually decay due to gravitational radiation and tunneling. They appear as narrow resonances in the heavy-light OPE when the spectrum becomes effectively continuous due to the presence of the black hole horizon. Alternatively, they can be identified with quasi-normal modes with small imaginary part in the thermal two-point function. The two pictures are related via the eigenstate thermalisation hypothesis. When the decay effects can be neglected the orbits appear as a discrete family of double-twist operators. We investigate the connection between orbits, quasi-normal modes, and double-twist operators in detail. Using the corrected Bohr-Sommerfeld formula for quasi-normal modes, we compute the anomalous dimension of double-twist operators. We compare our results to the prediction of the light-cone bootstrap, finding perfect agreement where the results overlap. We also compute the orbit decay time due to scalar radiation and compare it to the tunneling rate. Perturbatively in spin, in the light-cone bootstrap framework double-twist operators appear as a small fraction of the Hilbert space which violate the eigenstate thermalization hypothesis, a phenomenon known as many-body scars. Nonperturbatively in spin, the double-twist operators become long-lived states that eventually thermalize. We briefly discuss the connection between perturbative scars in holographic theories and known examples of scars in the condensed matter literature.Comment: 45 pages + appendices, 4 figure

New solutions with accelerated expansion in string theory

Abstract: We present concrete solutions with accelerated expansion in string theory, requiring a small, tractable list of stress energy sources. We explain how this construction (and others in progress) evades previous no go theorems for simple accelerating solutions. Our solutions respect an approximate scaling symmetry and realize discrete sequences of values for the equation of state, including one with an accumulation point at w = −1 and another accumulating near w = −1/3 from below. In another class of models, a density of defects generates scaling solutions with accelerated expansion. We briefly discuss potential applications to dark energy phenomenology, and to holography for cosmology.Fil: Dodelson, Matthew. University of Stanford; Estados UnidosFil: Dong, Xi. University of Stanford; Estados UnidosFil: Silverstein, Eva. University of Stanford; Estados Unidos. Fermi National Accelerator Laboratory; Estados UnidosFil: Torroba, Gonzalo. University of Stanford; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin

Black hole bulk-cone singularities

Lorentzian correlators of local operators exhibit surprising singularities in theories with gravity duals. These are associated with null geodesics in an emergent bulk geometry. We analyze singularities of the thermal response function dual to propagation of waves on the AdS Schwarzschild black hole background. We derive the analytic form of the leading singularity dual to a bulk geodesic that winds around the black hole. Remarkably, it exhibits a boundary group velocity larger than the speed of light, whose dual is the angular velocity of null geodesics at the photon sphere. The strength of this singularity is controlled by the classical Lyapunov exponent associated with the instability of nearly bound photon orbits. In this sense, the bulk-cone singularity can be identified as the universal feature that encodes the ubiquitous black hole photon sphere in a dual holographic CFT. To perform the computation analytically, we express the two-point correlator as an infinite sum over Regge poles, and then evaluate this sum using WKB methods. We also compute the smeared correlator numerically, which in particular allows us to check and support our analytic predictions. We comment on the resolution of black hole bulk-cone singularities by stringy and gravitational effects into black hole bulk-cone "bumps". We conclude that these bumps are robust, and could serve as a target for simulations of black hole-like geometries in table-top experiments.Comment: 63 pages, 17 figure

Holographic thermal correlators from supersymmetric instantons

We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement.Comment: 9 pages + appendices, 2 figures. v2: typos corrected, references adde

Effective String Theory and Nonlinear Lorentz Invariance

We study the low-energy effective action governing the transverse fluctuations of a long string, such as a confining flux tube in QCD. We work in the static gauge where this action contains only the transverse excitations of the string. The static gauge action is strongly constrained by the requirement that the Lorentz symmetry, that is spontaneously broken by the long string vacuum, is nonlinearly realized on the Nambu-Goldstone bosons. One solution to the constraints (at the classical level) is the Nambu-Goto action, and the general solution contains higher derivative corrections to this. We show that in 2+1 dimensions, the first allowed correction to the Nambu-Goto action is proportional to the squared curvature of the induced metric on the worldsheet. In higher dimensions, there is a more complicated allowed correction that appears at lower order than the curvature squared. We argue that this leading correction is similar to, but not identical to, the one-loop determinant (\sqrt{-h} R \Box^{-1} R) computed by Polyakov for the bosonic fundamental string.Comment: 15 page

Searching for dark matter in X-rays: how to check the dark matter origin of a spectral feature

A signal from decaying dark matter (DM) can be unambiguously distinguished from spectral features of astrophysical or instrumental origin by studying its spatial distribution. We demonstrate this approach by examining the recent claim of 0912.0552 regarding the possible DM origin of the 2.5 keV line in Chandra observations of the Milky Way satellite known as Willman 1. Our conservative strategy is to adopt a relatively large dark mass for Willman 1 and relatively small dark masses for the comparison objects. We analyze archival observations by XMM-Newton of M31 and Fornax dwarf spheroidal galaxy (dSph) and Chandra observations of Sculptor dSph. By performing a conservative analysis of X-ray spectra, we show the absence of a DM decay line with parameters consistent with those of 0912.0552. For M31, the observations of the regions between 10 and 20 kpc from the center, where the uncertainties in the DM distribution are minimal, make a strong exclusion at the level above 10sigma. The minimal estimate for the amount of DM in the central 40 kpc of M31 is provided by the model of 0912.4133, assuming the stellar disk's mass to light ratio ~8 and almost constant DM density within a core of 28 kpc. Even in this case one gets an exclusion at 5.7sigma from central region of M31 whereas modeling all processed data from M31 and Fornax produces more than 14sigma exclusion. Therefore, despite possible systematic uncertainties, we exclude the possibility that the spectral feature at ~2.5 keV found in 0912.0552 is a DM decay line. We conclude, however, that the search for DM decay line, although demanding prolonged observations of well-studied dSphs, M31 outskirts and other similar objects, is rather promising, as the nature of a possible signal can be checked. An (expected) non-observation of a DM decay signal in the planned observations of Willman 1 should not discourage further dedicated observations.Comment: 16 pages, 8 figures; journal version; analysis of additional data from M31 outskirts and comments on arXiv:1001.4055 are adde