arXiv subjects
Publications and source records attributed to Raman Sundrum.
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.
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.
We show that in a general hidden sector model, supersymmetry breaking necessarily generates at one-loop a scalar and gaugino mass as a consequence of the super-Weyl anomaly. We study a scenario in which this contribution dominates. We consider the Standard Model particles to be localized on a (3+1)-dimensional subspace or ``3-brane'' of a higher dimensional spacetime, while supersymmetry breaking occurs off the 3-brane, either in the bulk or on another 3-brane. At least one extra dimension is assumed to be compactified roughly one to two orders of magnitude below the four-dimensional Planck scale. This framework is phenomenologically very attractive; it introduces new possibilities for solving the supersymmetric flavor problem, the gaugino mass problem, the supersymmetric CP problem, and the mu-problem. Furthermore, the compactification scale can be consistent with a unification of gauge and gravitational couplings. We demonstrate these claims in a four-dimensional effective theory below the compactification scale that incorporates the relevant features of the underlying higher dimensional theory and the contribution of the super-Weyl anomaly. Naturalness constraints follow not only from symmetries but also from the higher dimensional origins of the theory. We also introduce additional bulk contributions to the MSSM soft masses. This scenario is very predictive: the gaugino masses, squark masses, and $A$ terms are given in terms of MSSM renormalization group functions.
A general effective field theory formalism is presented which describes the low-energy dynamics of a 3-brane universe. In this scenario an arbitrary four-dimensional particle theory, such as the Standard Model, is constrained to live on the world-volume of a (3+1)-dimensional hypersurface, or ``3-brane'', which in turn fluctuates in a higher-dimensional, gravitating spacetime. The inclusion of chiral fermions on the 3-brane is given careful treatment. The power-counting needed to renormalize quantum amplitudes of the effective theory is also discussed. The effective theory has a finite domain of validity, restricting it to processes at low enough energies that the internal structure of the 3-brane cannot be resolved.
A fully realistic and systematic effective field theory model of a 3-brane universe is constructed. It consists of a six-dimensional gravitating spacetime, containing several, approximately parallel (3+1)-dimensional defects, or ``3-branes''. The Standard Model particles are confined to live on one of the 3-branes while different four-dimensional field theories may inhabit the others, in literally a case of ``parallel universes''. The effective field theory is valid up to the six-dimensional Planck scale, where it must be replaced by a more fundamental theory of gravity and 3-brane structure. Each 3-brane induces a conical geometry in the two dimensions transverse to it. Collectively, the curvature induced by the 3-branes can compactify the extra dimensions into a space of spherical topology. It is possible to take the six-dimensional Planck scale to be not much larger than the weak scale, and the compact space not much smaller than a millimeter, thereby realizing the recent proposal by Arkani-Hamed, Dimopoulos and Dvali for eliminating the Gauge Hierearchy Problem. In this case, an extra force is required to stabilize the compact space against collapse. This is provided by a six-dimensional (compact) U(1) gauge field with a magnetic flux quantum trapped in the compact space. The nature of the Cosmological Constant Problem in this scenario is discussed.
The Cosmological Constant Problem is re-examined from an effective field theory perspective. While the connection between gravity and particle physics has not been experimentally probed in the quantum regime, it is severely constrained by the successes of Standard Model quantum field theory at short distances, and classical General Relativity at large distances. At first sight, it appears that combining particle physics and gravity inevitably leads to an effective field theory below the weak scale which suffers from large radiative corrections to the cosmological constant. Consequently, this parameter must be very finely tuned to lie within the experimental bounds. An analog of just this type of predicament, and its resolution, are described in some detail using only familiar quantum field theory. The loop-hole abstracted from the analogy is the possibility of graviton ``compositeness'' at a scale less than $10^{-2}$ eV, which cuts off the large contributions to the cosmological constant from standard model physics. Experimentally, this would show up as a dramatic breakdown of Newton's Law in upcoming sub-centimeter tests of gravity. Currently, strings are the only known example of such compositeness. It is proposed that the gravitational sector comprises strings of very low tension, which couple to a stringy ``halo'' surrounding each point-like standard model particle.
Heavy Quark Effective Theory splits a heavy quark momentum into a large fixed momentum and a variable residual momentum, p = m_Q v + k. It thereby suffers a redundancy of description corresponding to small changes in the choice of the fixed velocity, v. The fact that full QCD is manifestly v-independent should lead to a non-trivial constraint on the form of the effective theory, known as Reparameterization Invariance. For spin-1/2 quarks, the precise form of the constraint and its solution at the level of the effective lagrangian have proven to be rather subtle, and the original proposal by Luke and Manohar has been questioned. In this paper I employ a version of Heavy Quark Effective Theory containing the ``anti-particle'' field as a non-propagating auxiliary field, which greatly simplifies keeping track of v-dependence. This permits a very simple derivation of Reparameterization Invariance from first principles. The auxiliary field can also be integrated out to return to the standard formulation of the effective theory, but with the effective lagrangian now satisfying the full reparameterization constraint. I compare this result with earlier proposals.
We investigate Seiberg's N=1 field theory duality for four-dimensional supersymmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory configuration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in Type IIA string theory is given a nice derivation from M-theory.
The existence of hadronic string is derived as a consequence of confinement in QCD. A state of ``stretched glue'', created by a Polyakov loop operator, is shown to have translational zero-modes which are stringy degrees of freedom. These modes are described by an effective string theory, valid for world- sheets which are locally flat on length scales of order $Λ_{QCD}^{-1}$, the dominant behavior being given by the Nambu-Goto action. In a subsequent paper, these effective strings will be shown to emerge in mesons stretched by their orbital angular momentum, thereby deriving some aspects of Regge phenomenology directly from QCD and confinement.
We review our recent proposal for a new lattice action for non-abelian gauge theories which reduces short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. We illustrate the improved behavior of a same-philosophy new lattice action in the $O(3)$ $σ$-model in two dimensions.
The importance of lattice gauge field interpolation for our recent non-perturbative formulation of chiral gauge theory is emphasized. We illustrate how the requisite properties are satisfied by our recent four-dimensional non-abelian interpolation scheme, by going through the simpler case of U(1) gauge fields in two dimensions.
We propose a method for interpolating non-abelian lattice gauge fields to the continuum, or to a finer lattice, which satisfies the properties of (i) transverse continuity, (ii) (lattice) rotation and translation covariance, (iii) gauge covariance, (iv) locality. These are the properties required for use in our earlier proposal for non-perturbative formulation and simulation of chiral gauge theories.
We propose a new lattice action for non-abelian gauge theories, which will reduce short-range lattice artifacts in the computation of the topological susceptibility. The standard Wilson action is replaced by the Wilson action of a gauge covariant interpolation of the original fields to a finer lattice. If the latter is fine enough, the action of all configurations with non-zero topological charge will satisfy the continuum bound. As a simpler example we consider the $O(3)$ $σ$-model in two dimensions, where a numerical analysis of discretized continuum instantons indicates that a finer lattice with half the lattice spacing of the original is enough to satisfy the continuum bound.
We discuss the problem of formulating the continuum limit of chiral gauge theories ($χ$GT) in the absence of an explicitly gauge-invariant regulator for the fermions. A solution is proposed which is independent of the details of the regulator, wherein one considers two cutoff scales, $Λ_f >> Λ_b$, for the fermions and the gauge bosons respectively. Our recent non-perturbative lattice construction in which the fermions live on a finer lattice than do the gauge bosons, is seen to be an example of such a scheme, providing a finite algorithm for simulating $χ$GT. The essential difference with previous (one-cutoff) lattice schemes is clarified: in our formulation the breakage of gauge invariance is small, $O(Λ^2_b/Λ^2_f)$, and vanishes in the continuum limit. Finally, we argue against 2-D models being significant testing grounds for 4-D regulators of $χ$GT.
We formulate chiral gauge theories non-perturbatively, using two different cuttoffs for the fermions and gauge bosons. We use a lattice with spacing $b$ to regulate the gauge fields in standard fashion, while computing the chiral fermion determinant on a finer lattice with spacing $f << b$. This determinant is computed in the background of $f$-lattice gauge fields, obtained by gauge-covariantly interpolating $b$-lattice gauge fields. The notorious doublers that plague lattice theories containing fermions are decoupled by the addition of a Wilson term. In chiral theories such a term breaks gauge invariance explicitly. However, the advantage of the two-cutoff regulator is that gauge invariance can be restored to $O(f^2/b^2)$ by a {\it one-loop} subtraction of calculable local gauge field counterterms. We show that the only obstruction to this procedure is the presence of an uncancelled gauge anomaly among the fermion representations. We conclude that for practical purposes, it suffices to choose $f/b \sim b/L$, where $L^4$ is the physical volume of the system. In our construction it is simple to prove the Adler-Bardeen theorem for anomalies in global currents to all orders. The related subject of fermion number violation is also studied. Finally, we discuss the prospects for improving the efficiency of our algorithm.
We use the observed $SU(3)$ breaking in the mass spectrum of mesons containing a single heavy quark to place restrictions on the light quark current masses. A crucial ingredient in this analysis is our recent first-principles calculation of the electromagnetic contribution to the isospin-violating mass splittings. We also pay special attention to the role of higher-order corrections in chiral perturbation theory. We find that large corrections are necessary for the heavy meson data to be consistent with $m_u = 0$.
We compute the electromagnetic mass differences of mesons containing a single heavy quark in terms of measurable data using QCD-based arguments in heavy-quark effective theory. We derive an unsubtracted dispersion relation that shows that the mass differences are calculable in terms of the properties of the lowest-lying physical intermediate states. We then consider the problem in the large-$N$ limit, where $N$ is the number of QCD colors. In this limit, we can write a kind of double-dispersion relation for the amplitude required to determine the electromagnetic mass difference. We use this to derive analogs of the Weinberg sum rules for heavy meson matrix elements valid to leading order in $1/N$ and to $O(1/m_Q)$ in the heavy quark expansion. In order to obtain our final result, we assume that the electromagnetic mass differences and sum rules are dominated by the lowest-lying states in analogy with the situation for the $π^+$--$π^0$ mass difference. Despite the fact that some of the matrix elements appearing in our final result have not yet been accurately measured, we can obtain useful numerical estimates: for example, we obtain $(M_{B^+} - M_{B^0})^{EM} \simeq +1.8 \MeV$. We argue that our results are accurate to about $30\%$.
The rates of the rare flavor-changing processes, $b \rightarrow s γ$ and $B_s \rightarrow μ^+ μ^-$ are estimated in extended technicolor models with and without a GIM mechanism. We find the $b \rightarrow s γ$ rate in ETC models with a GIM mechanism to be at most slightly larger than the standard model rate, whereas there is no significant extra model-independent contribution in other ETC scenarios. In the case of $B_s \rightarrow μ^+ μ^-$, ETC models with a GIM mechanism can yield a rate up to two orders of magnitude bigger than that of the standard model, whereas generic ETC scenarios are likely to give a rate which is about an order of magnitude bigger than that of the standard model.