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      Heat kernel expansion: user's manual

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          Abstract

          The heat kernel expansion is a very convenient tool for studying one-loop divergences, anomalies and various asymptotics of the effective action. The aim of this report is to collect useful information on the heat kernel coefficients scattered in mathematical and physical literature. We present explicit expressions for these coefficients on manifolds with and without boundaries, subject to local and non-local boundary conditions, in the presence of various types of singularities (e.g., domain walls). In each case the heat kernel coefficients are given in terms of several geometric invariants. These invariants are derived for scalar and spinor theories with various interactions, Yang-Mills fields, gravity, and open bosonic strings. We discuss the relations between the heat kernel coefficients and quantum anomalies, corresponding anomalous actions, and covariant perturbation expansions of the effective action (both "low-" and "high-energy" ones).

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          A Large Mass Hierarchy from a Small Extra Dimension

          We propose a new higher-dimensional mechanism for solving the Hierarchy Problem. The Weak scale is generated from a large scale of order the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of AdS_5 spacetime). This mechanism relies on the existence of only a single additional dimension. We demonstrate a simple explicit example of this mechanism with two three-branes, one of which contains the Standard Model fields. The experimental consequences of this scenario are new and dramatic. There are fundamental spin-2 excitations with mass of weak scale order, which are coupled with weak scale as opposed to gravitational strength to the standard model particles. The phenomenology of these models is quite distinct from that of large extra dimension scenarios; none of the current constraints on theories with very large extra dimensions apply.
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            An Alternative to Compactification

            Conventional wisdom states that Newton's force law implies only four non-compact dimensions. We demonstrate that this is not necessarily true in the presence of a non-factorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.
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              Quantum Theory of Gravity. I. The Canonical Theory

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                Author and article information

                Journal
                2003-06-15
                2003-09-06
                Article
                10.1016/j.physrep.2003.09.002
                hep-th/0306138
                f5397a5a-901a-450c-85b6-099cb7a48c09
                History
                Custom metadata
                Phys.Rept.388:279-360,2003
                113 pp, to be submitted to Phys.Repts, v2: added references and corrected typos
                hep-th cond-mat hep-ph math-ph math.MP

                Mathematical physics,Condensed matter,High energy & Particle physics,Mathematical & Computational physics

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