Maxim Perelstein

On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences

String theory implies that field theories containing gravity are in a certain sense ‘products’ of gauge theories. We make this product structure explicit up to two loops for the relatively simple case of N = 8 supergravity four-point amplitudes, demonstrating that they are ‘squares’ of N = 4 super-Yang-Mills amplitudes. This is accomplished by obtaining an explicit expression for the Ddimensional two-loop contribution to the four-particle S-matrix for N = 8 supergravity, which we compare to the corresponding N = 4 Yang-Mills result. From these expressions we also obtain the two-loop ultraviolet divergences in dimensions D = 7 through D = 11. The analysis relies on the unitarity cuts of the two theories, many of which can be recycled from a one-loop computation. The two-particle cuts, which may be iterated to all loop orders, suggest that squaring relations between the two theories exist at any loop order. The loop-momentum power-counting implied by our two-particle cut analysis indicates that in four dimensions the first four-point divergence in N = 8 supergravity should appear at five loops, contrary to the earlier expectation, based on superspace arguments, of a three-loop counterterm.

Little Higgs models and their phenomenology

This article reviews the Little Higgs models of electroweak symmetry breaking and their phenomenology. Little Higgs models incorporate a light composite Higgs boson and remain perturbative until a scale of order 10 TeV, as required by precision electroweak data. The collective symmetry breaking mechanism, which forms the basis of Little Higgs models, is introduced. An explicit, fully realistic implementation of this mechanism, the Littlest Higgs model, is then discussed in some detail. Several other implementations, including simple group models and models with T parity, are also reviewed. Precision electroweak constraints on a variety of Little Higgs models are summarized. If a Little Higgs model is realized in nature, the predicted new particles should be observable at the Large Hadron Collider (LHC). The expected signatures, as well as the experimental sensitivities and the possible strategies for confirming the Little Higgs origin of new particles, are discussed. Finally, several other related topics are briefly reviewed, including the ultraviolet completions of Little Higgs models, as well as the implications of these models for flavor physics and cosmology.

Collider signatures of new large space dimensions

Recently, Arkani-Hamed, Dimopoulos, and Dvali have proposed that there are extra compact dimensions of space, accessible to gravity but not to ordinary matter, which could be macroscopically large. In this letter, we argue that high-energy collider processes in which gravitons are radiated into these new dimensions place significant, model-independent constraints on this picture. We present the constraints from anomalous single photon production at e{sup +}e{sup {minus}} colliders and from monojet production at hadron colliders.

Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory

Abstract By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n -graviton scattering amplitudes: the ‘maximally helicity-violating’ amplitudes in N = 8 supergravity, and the ‘all-plus’ helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n ⩽ 6, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found ‘dimension-shifting’ relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N = 4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n ⩽ 6 N = 8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations.

SN 1987A Constraints on Large Compact Dimensions

Recently there has been a lot of interest in models in which gravity becomes strong at the TeV scale. The observed weakness of gravitational interactions is then explained by the existence of extra compact dimensions of space, which are accessible to gravity but not to standard model particles. We consider graviton emission into these extra dimensions from a hot supernova core. The phenomenology of SN 1987A places strong constraints on this energy loss mechanism, allowing us to derive a bound on the fundamental Planck scale. For the case of two extra dimensions we obtain a very strong bound of

TeV strings and collider probes of large extra dimensions

M\ensuremath{\gtrsim}50\mathrm{TeV}

Electroweak precision constraints on the littlest Higgs model with T parity

, which corresponds to a radius

Dark matter at colliders: A Model independent approach

R\ensuremath{\lesssim}0.3\ensuremath{\mu}\mathrm{m}

Little Higgs dark matter

.

Neutralino annihilation into two photons

Arkani-Hamed, Dimopoulos, and Dvali have proposed that the fundamental gravitational scale is close to 1 TeV, and that the observed weakness of gravity at long distances is explained by the presence of large extra compact dimensions. If this scenario is realized in a string theory of quantum gravity, the string excited states of standard model particles will also have TeV masses. These states will be visible to experiment and in fact provide the first signatures of the presence of a low quantum gravity scale. Their presence also affects the more familiar signatures due to real and virtual graviton emission. We study the effects of these states in a simple string model. (c) 2000 The American Physical Society.