Hidden Simplicity of the Gravity Action

We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons and a single auxiliary field. The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. Since all Feynman diagrams are cubic, we are able to derive new off-shell recursion relations for tree-level graviton scattering amplitudes. With a judicious choice of gauge fixing, we then construct an especially compact form for the Einstein-Hilbert action in which all graviton interactions are simply proportional to the graviton kinetic term. Our results apply to graviton perturbations about an arbitrary curved background spacetime.Comment: 20 pages, 1 figur

Nucleus accumbens core lesions retard instrumental learning and performance with delayed reinforcement in the rat.

BACKGROUND: Delays between actions and their outcomes severely hinder reinforcement learning systems, but little is known of the neural mechanism by which animals overcome this problem and bridge such delays. The nucleus accumbens core (AcbC), part of the ventral striatum, is required for normal preference for a large, delayed reward over a small, immediate reward (self-controlled choice) in rats, but the reason for this is unclear. We investigated the role of the AcbC in learning a free-operant instrumental response using delayed reinforcement, performance of a previously-learned response for delayed reinforcement, and assessment of the relative magnitudes of two different rewards. RESULTS: Groups of rats with excitotoxic or sham lesions of the AcbC acquired an instrumental response with different delays (0, 10, or 20 s) between the lever-press response and reinforcer delivery. A second (inactive) lever was also present, but responding on it was never reinforced. As expected, the delays retarded learning in normal rats. AcbC lesions did not hinder learning in the absence of delays, but AcbC-lesioned rats were impaired in learning when there was a delay, relative to sham-operated controls. All groups eventually acquired the response and discriminated the active lever from the inactive lever to some degree. Rats were subsequently trained to discriminate reinforcers of different magnitudes. AcbC-lesioned rats were more sensitive to differences in reinforcer magnitude than sham-operated controls, suggesting that the deficit in self-controlled choice previously observed in such rats was a consequence of reduced preference for delayed rewards relative to immediate rewards, not of reduced preference for large rewards relative to small rewards. AcbC lesions also impaired the performance of a previously-learned instrumental response in a delay-dependent fashion. CONCLUSIONS: These results demonstrate that the AcbC contributes to instrumental learning and performance by bridging delays between subjects' actions and the ensuing outcomes that reinforce behaviour

Quantum Gravity Constraints from Unitarity and Analyticity

We derive rigorous bounds on corrections to Einstein gravity using unitarity and analyticity of graviton scattering amplitudes. In $D\geq 4$ spacetime dimensions, these consistency conditions mandate positive coefficients for certain quartic curvature operators. We systematically enumerate all such positivity bounds in $D=4$ and $D=5$ before extending to $D\geq 6$. Afterwards, we derive positivity bounds for supersymmetric operators and verify that all of our constraints are satisfied by weakly-coupled string theories. Among quadratic curvature operators, we find that the Gauss-Bonnet term in $D\geq 5$ is inconsistent unless new degrees of freedom enter at the natural cutoff scale defined by the effective theory. Our bounds apply to perturbative ultraviolet completions of gravity.Comment: 26 page

Proof of the Weak Gravity Conjecture from Black Hole Entropy

We prove that higher-dimension operators contribute positively to the entropy of a thermodynamically stable black hole at fixed mass and charge. Our results apply whenever the dominant corrections originate at tree level from quantum field theoretic dynamics. More generally, positivity of the entropy shift is equivalent to a certain inequality relating the free energies of black holes. These entropy inequalities mandate new positivity bounds on the coefficients of higher-dimension operators. One of these conditions implies that the charge-to-mass ratio of an extremal black hole asymptotes to unity from above for increasing mass. Consequently, large extremal black holes are unstable to decay to smaller extremal black holes and the weak gravity conjecture is automatically satisfied. Our findings generalize to arbitrary spacetime dimension and to the case of multiple gauge fields. The assumptions of this proof are valid across a range of scenarios, including string theory constructions with a dilaton stabilized below the string scale.Comment: 35 pages, 2 figure

Infrared Consistency and the Weak Gravity Conjecture

The weak gravity conjecture (WGC) asserts that an Abelian gauge theory coupled to gravity is inconsistent unless it contains a particle of charge $q$ and mass $m$ such that $q \geq m/m_{\rm Pl}$. This criterion is obeyed by all known ultraviolet completions and is needed to evade pathologies from stable black hole remnants. In this paper, we explore the WGC from the perspective of low-energy effective field theory. Below the charged particle threshold, the effective action describes a photon and graviton interacting via higher-dimension operators. We derive infrared consistency conditions on the parameters of the effective action using i) analyticity of light-by-light scattering, ii) unitarity of the dynamics of an arbitrary ultraviolet completion, and iii) absence of superluminality and causality violation in certain non-trivial backgrounds. For convenience, we begin our analysis in three spacetime dimensions, where gravity is non-dynamical but has a physical effect on photon-photon interactions. We then consider four dimensions, where propagating gravity substantially complicates all of our arguments, but bounds can still be derived. Operators in the effective action arise from two types of diagrams: those that involve electromagnetic interactions (parameterized by a charge-to-mass ratio $q/m$) and those that do not (parameterized by a coefficient $\gamma$). Infrared consistency implies that $q/m$ is bounded from below for small $\gamma$.Comment: 37 pages, 5 figures. Minor typos fixed and equation numbers changed to match journal. Published in JHE

Vocal learning promotes patterned inhibitory connectivity.

Skill learning is instantiated by changes to functional connectivity within premotor circuits, but whether the specificity of learning depends on structured changes to inhibitory circuitry remains unclear. We used slice electrophysiology to measure connectivity changes associated with song learning in the avian analog of primary motor cortex (robust nucleus of the arcopallium, RA) in Bengalese Finches. Before song learning, fast-spiking interneurons (FSIs) densely innervated glutamatergic projection neurons (PNs) with apparently random connectivity. After learning, there was a profound reduction in the overall strength and number of inhibitory connections, but this was accompanied by a more than two-fold enrichment in reciprocal FSI-PN connections. Moreover, in singing birds, we found that pharmacological manipulations of RA's inhibitory circuitry drove large shifts in learned vocal features, such as pitch and amplitude, without grossly disrupting the song. Our results indicate that skill learning establishes nonrandom inhibitory connectivity, and implicates this patterning in encoding specific features of learned movements

A heuristic approach for multiple restricted multiplication

Published versio

Amplitudes and Spinor-Helicity in Six Dimensions

The spinor-helicity formalism has become an invaluable tool for understanding the S-matrix of massless particles in four dimensions. In this paper we construct a spinor-helicity formalism in six dimensions, and apply it to derive compact expressions for the three, four and five point tree amplitudes of Yang-Mills theory. Using the KLT relations, it is a straightforward process to obtain amplitudes in linearized gravity from these Yang-Mills amplitudes; we demonstrate this by writing down the gravitational three and four point amplitudes. Because there is no conserved helicity in six dimensions, these amplitudes describe the scattering of all possible polarization states (as well as Kaluza-Klein excitations) in four dimensions upon dimensional reduction. We also briefly discuss a convenient formulation of the BCFW recursion relations in higher dimensions.Comment: 26 pages, 2 figures. Minor improvements of the discussio