Constraints on parity violating conformal field theories in d=3d=3

We derive constraints on three-point functions involving the stress tensor, $T$, and a conserved $U(1)$ current, $j$, in 2+1 dimensional conformal field theories that violate parity, using conformal collider bounds introduced by Hofman and Maldacena. Conformal invariance allows parity-odd tensor-structures for the $\langle T T T \rangle$ and $\langle j j T \rangle$ correlation functions which are unique to three space-time dimensions. Let the parameters which determine the $\langle T T T \rangle$ correlation function be $t_4$ and $\alpha_T$ , where $\alpha_T$ is the parity-violating contribution. Similarly let the parameters which determine $\langle j j T \rangle$ correlation function be $a_2$, and $\alpha_J$ , where $\alpha_J$ is the parity-violating contribution. We show that the parameters $(t_4, \alpha_T)$ and $(a_2, \alpha_J)$ are bounded to lie inside a disc at the origin of the $t_4$ - $\alpha_T$ plane and the $a_2$ - $\alpha_J$ plane respectively. We then show that large $N$ Chern-Simons theories coupled to a fundamental fermion/boson lie on the circle which bounds these discs. The `t Hooft coupling determines the location of these theories on the boundary circles.Comment: Minor typos corrected, Figures changed , References adde

Bootstrap and collider physics of parity violating conformal field theories in d=3d=3

We study the crossing equations in $d=3$ for the four point function of two $U(1)$ currents and two scalars including the presence of a parity violating term for the $s$-channel stress tensor exchange. We show the existence of a new tower of double trace operators in the $t$-channel whose presence is necessary for the crossing equation to be satisfied and determine the corresponding large spin parity violating OPE coefficients. Contrary to the parity even situation, we find that the parity odd $s$-channel light cone stress tensor block do not have logarithmic singularities. This implies that the parity odd term does not contribute to anomalous dimensions in the crossed channel at this order in light cone expansion. We then study the constraints imposed by reflection positivity and crossing symmetry on such a four point function. We reproduce the previously known parity odd collider bounds through this analysis. The contribution of the parity violating term in the collider bound results from a square root branch cut present in the light cone block as opposed to a logarithmic cut in the parity even case, together with the application of the Cauchy-Schwarz inequality.Comment: References update

Spectral sum rules for conformal field theories in arbitrary dimensions

We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general $d\geq 3$ dimensions. The sum rules result from the OPE of the stress tensor at high frequency as well as the hydrodynamic behaviour of the theory at low frequencies. The sum rule states that a weighted integral of the spectral density over frequencies is proportional to the energy density of the theory. We show that the proportionality constant can be written in terms the Hofman-Maldacena variables $t_2, t_4$ which determine the three point function of the stress tensor. For theories which admit a two derivative gravity dual this proportionality constant is given by $\frac{d}{2(d+1)}$. We then use causality constraints and obtain bounds on the sum rule which are valid in any conformal field theory. Finally we demonstrate that the high frequency behaviour of the spectral function in the vector and the tensor channel are also determined by the Hofman-Maldacena variables.Comment: Corrected typos, JHEP versio

Sunyaev-Zel'dovich Signal from Quasar Hosts: Implications for Detection of Quasar Feedback

Several analytic and numerical studies have indicated that the interstellar medium of a quasar host galaxy heated by feedback can contribute to a substantial secondary signal in the cosmic microwave background (CMB) through the thermal Sunyaev-Zel'dovich (SZ) effect. Recently, many groups have tried to detect this signal by cross-correlating CMB maps with quasar catalogs. Using a self-similar model for the gas in the intra-cluster medium and a realistic halo occupation distribution (HOD) prescription for quasars we estimate the level of SZ signal from gravitational heating of quasar hosts. The bias in the host halo signal estimation due to unconstrained high mass HOD tail and yet unknown redshift dependence of the quasar HOD restricts us from drawing any robust conclusions at low redshift (z<1.5) from our analysis. However, at higher redshifts (z>2.5), we find an excess signal in recent observations than what is predicted from our model. The excess signal could be potentially generated from additional heating due to quasar feedback.Comment: 6 pages, 3 figures, accepted for publication in Ap

Effect of external electric field on the charge density waves in one dimensional Hubbard superlattices

We have studied the ground state of the one dimensional Hubbard superlattice structures with different unit cell sizes in the presence of electric field. Self consistent Hartree-Fock approximation calculation is done in the weak to intermediate interaction regime. Studying the charge gap at the Fermi level and the charge density structure factor, we get an idea how the charge modulation on the superlattice is governed by the competition between the electronic correlation and the external electric field.Comment: 6 pages, 8 figures. accepted in Journal of Physics: Condensed Matte