Constraints from Conformal Symmetry on the Three Point Scalar Correlator in Inflation

Using symmetry considerations, we derive Ward identities which relate the three point function of scalar perturbations produced during inflation to the scalar four point function, in a particular limit. The derivation assumes approximate conformal invariance, and the conditions for the slow roll approximation, but is otherwise model independent. The Ward identities allow us to deduce that the three point function must be suppressed in general, being of the same order of magnitude as in the slow roll model. They also fix the three point function in terms of the four point function, upto one constant which we argue is generically suppressed. Our approach is based on analyzing the wave function of the universe, and the Ward identities arise by imposing the requirements of spatial and time reparametrization invariance on it.Comment: 35 pages; Extra references and comments added, The version published in JHE

Ward Identities for Scale and Special Conformal Transformations in Inflation

We derive the general Ward identities for scale and special conformal transformations in theories of single field inflation. Our analysis is model independent and based on symmetry considerations alone. The identities we obtain are valid to all orders in the slow roll expansion. For special conformal transformations, the Ward identities include a term which is non-linear in the fields that arises due to a compensating spatial reparametrization. Some observational consequences are also discussed.Comment: 42 Pages. v3: Section on checks of the Ward identities added. The JHEP accepted versio

Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes

We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or $AdS_2 \times S^3$ geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or $AdS_2 \times S^3$ geometries can in turn be connected to $AdS_5$ spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to $AdS_5$ spacetime. The asymptotic $AdS_5$ spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points.Comment: 37 pages, 12 figures, The comment regarding the behavior of C-function for general Bianchi Types appearing in IR or UV clarified, the relation of Type IX with $AdS_2 \times S^3$ for $\lambda=1$ made more precise and a comment regarding type V added in the conclusio

Modeling the Impact of Process Variation on Resistive Bridge Defects

Recent research has shown that tests generated without taking process variation into account may lead to loss of test quality. At present there is no efficient device-level modeling technique that models the effect of process variation on resistive bridges. This paper presents a fast and accurate technique to model the effect of process variation on resistive bridge defects. The proposed model is implemented in two stages: firstly, it employs an accurate transistor model (BSIM4) to calculate the critical resistance of a bridge; secondly, the effect of process variation is incorporated in this model by using three transistor parameters: gate length (L), threshold voltage (V) and effective mobility (ueff) where each follow Gaussian distribution. Experiments are conducted on a 65-nm gate library (for illustration purposes), and results show that on average the proposed modeling technique is more than 7 times faster and in the worst case, error in bridge critical resistance is 0.8% when compared with HSPICE

On Improving Reliability of SRAM-Based Physically Unclonable Functions

Physically unclonable functions (PUFs) have been touted for their inherent resistance to invasive attacks and low cost in providing a hardware root of trust for various security applications. SRAM PUFs in particular are popular in industry for key/ID generation. Due to intrinsic process variations, SRAM cells, ideally, tend to have the same start-up behavior. SRAM PUFs exploit this start-up behavior. Unfortunately, not all SRAM cells exhibit reliable start-up behavior due to noise susceptibility. Hence, design enhancements are needed for improving reliability. Some of the proposed enhancements in literature include fuzzy extraction, error-correcting codes and voting mechanisms. All enhancements involve a trade-off between area/power/performance overhead and PUF reliability. This paper presents a design enhancement technique for reliability that improves upon previous solutions. We present simulation results to quantify improvement in SRAM PUF reliability and efficiency. The proposed technique is shown to generate a 128-bit key in ≤0.2 μ\u27\u3eμμ s at an area estimate of 4538 μ\u27\u3eμμ m 2\u27\u3e22 with error rate as low as 10−6\u27\u3e10−610−6 for intrinsic error probability of 15%

Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes, and a Classification for the Homogeneous Case

Classifying the zero-temperature ground states of quantum field theories with finite charge density is a very interesting problem. Via holography, this problem is mapped to the classification of extremal charged black brane geometries with anti-de Sitter asymptotics. In a recent paper [1], we proposed a Bianchi classification of the extremal near-horizon geometries in five dimensions, in the case where they are homogeneous but, in general, anisotropic. Here, we extend our study in two directions: we show that Bianchi attractors can lead to new phases, and generalize the classification of homogeneous phases in a way suggested by holography. In the first direction, we show that hyperscaling violation can naturally be incorporated into the Bianchi horizons. We also find analytical examples of "striped" horizons. In the second direction, we propose a more complete classification of homogeneous horizon geometries where the natural mathematics involves real four-algebras with three dimensional sub-algebras. This gives rise to a richer set of possible near-horizon geometries, where the holographic radial direction is non-trivially intertwined with field theory spatial coordinates. We find examples of several of the new types in systems consisting of reasonably simple matter sectors coupled to gravity, while arguing that others are forbidden by the Null Energy Condition. Extremal horizons in four dimensions governed by three-algebras or four-algebras are also discussed.Comment: 58 pages, 1 figure and 1 cartoon. v2: references adde