119076672
D0 Matrix Mechanics: Topological Dynamics of Fuzzy Spaces
We consider the physics of a matrix model describing D0-brane dynamics in the presence of an RR flux background. Non-commuting spaces arise as generic soltions to this matrix model, among which fuzzy spheres have been studied extensively as static solutions at finite N. The existence of topologicaly distinct static configurations suggests the possibility of D-brane topology change within this model, however a dynamical solution interpolating between topologies is still somewhat elusive. In this paper, we study this model in the limit of infinite dimensional matrices, where new solutions-- the fuzzy cylinder and the fuzzy plane among them-- appear. We argue that any dynamics which involves topology change will likely only occur in this limit, after which we study the decay of a fuzzy cylinder into an infinite collection of fuzzy spheres as both a classical and a quantum phenomenon. We conclude from this excercise that in certain limits, matrix models offer a viable framework in which to study topological dynamics, and could perhaps be a precursor to a viable theory of space-time topological dynamics.
118490430
CMB imprints of a pre-inflationary climbing phase
We discuss the implications for cosmic microwave background (CMB) observables, of a class of pre-inflationary dynamics suggested by string models where SUSY is broken due to the presence of D-branes and orientifolds preserving incompatible portions of it. In these models the would-be inflaton is forced to emerge from the initial singularity climbing up a mild exponential potential, until it bounces against a steep exponential potential of ``brane SUSY breaking'' scenarios, and as a result the ensuing descent gives rise to an inflationary epoch that begins when the system is still well off its eventual attractor. If a pre-inflationary climbing phase of this type had occurred within 6-7 e-folds of the horizon exit for the largest observable wavelengths, displacement off the attractor and initial-state effects would conspire to suppress power in the primordial scalar spectrum, enhancing it in the tensor spectrum and typically superposing oscillations on both. We investigate these imprints on CMB observables over a range of parameters, examine their statistical significance, and provide a semi-analytic rationale for our results. It is tempting to ascribe at least part of the large-angle anomalies in the CMB to pre-inflationary dynamics of this type.
118823120
D0 matrix mechanics: New fuzzy solutions at large N
We wish to consider in this report the large-N limit of a particular matrix model introduced by Myers describing D-brane physics in the presence of an RR flux background. At finite N, fuzzy spheres appear naturally as non-trivial solutions to this matrix model and have been extensively studied. In this report, we wish to demonstrate several new classes of solutions which appear in the large-N limit, corresponding to the fuzzy cylinder,the fuzzy plane and a warped fuzzy plane. The latter two solutions arise from a possible ``central extension" to our model that arises after we account for non-trivial issues involved in the large-N limit. As is the case for finite N, these new solutions are to be interpreted as constituent D0-branes forming D2 bound states describing new fuzzy geometries.
119275413
On Semi-classical Degravitation and the Cosmological Constant Problems
In this report, we discuss a candidate mechanism through which one might address the various cosmological constant problems. We first observe that the renormalization of gravitational couplings (induced by integrating out various matter fields) manifests non-local modifications to Einstein’s equations as quantum corrected equations of motion. That is, at the loop level, matter sources curvature through a gravitational coupling that is a non-local function of the covariant d’Alembertian. If the functional form of the resulting Newton’s ‘constant’ is such that it annihilates very long wavelength sources, but reduces to 1=M 2 (Mpl being the 4d Planck mass) for all sources with cosmologically observable wavelengths, we would have a complimentary realization of the degravitation paradigm– a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider various theories whose coupling to gravity may a priori induce non-trivial renormalizations of Newton’s constant in the IR, and arrive at a class of non-local effective actions which yield a suitably degravitating filter function for Newton’s constant upon subsequently being integrated out. We motivate this class of non-local theories through several considerations, discuss open issues, future directions, the inevitable question of scheme dependence in semi-classical gravitational calculations and comment on connections with other meditations in the literature on relaxing of the cosmological constant semi-classically.
119039401
Exponential Inflation With $\rho = +p$
We introduce in this paper a new framework for obtaining a period of exponential inflation that is entirely driven by the quadratic kinetic energy of a scalar field. In contrast to recent attempts to realize scalar field inflation without potentials (such as k-inflation or ghost inflation), we find that it is possible to obtain exponential inflation, without invoking any higher derivative actions, or modifying gravity, and that unlike all previous approaches, we do not require a $\rho = -p$ phase in order to realize inflation. The inflaton in our proposed framework is a scalar field with a quadratic kinetic energy term, but with the `wrong sign'. We take the perspective that this is due to some temporary instability in our system at high energies, and provide physical examples of situations where a modulus field might temprorarily exhibit such behaviour. The deflation of extra dimensions is a neccesary feature of our framework. However, unlike in previous attempts at Kaluza-Klein inflation, it is possible to obtain exponential (as opposed to power law or pole) inflation. We provide several indications of how one can gracefully exit from this type of inflation.
119088066
UV/IR mode mixing and the CMB
It is well understood that spatial noncommutativity, if indeed realized in nature, is a phenomenon whose effects are not just felt at energy scales comparable to the noncommutativity scale. Loop effects can transmit signatures of any underlying noncommutativity to macroscopic scales (a manifestation of a phenomenon that has come to be known as UV/IR mode mixing) and offer a potential lever to constrain the amount of noncommutativity present in nature, if present at all. Field theories defined on noncommutative spaces (realized in string theory when D-branes are coupled to backgrounds of nontrivial RR background flux), can exhibit strong UV/IR mode mixing, manifesting in a nonlocal one-loop effective action. In the context of inflation in the presence of any background noncommutativity, we demonstrate how this UV/IR mixing at the loop level can allow us to place severe constraints on the scale of noncommutativity if we presume inflation is responsible for large-scale structure. We demonstrate that any amount of noncommutativity greatly suppresses the cosmic microwave background power at all observable scales, independent of the scale of inflation, and independent of whether or not the noncommutativity tensor redshifts during inflation, therefore nullifying a very salient and successful prediction of inflation.
119717796
A non-polynomial Lee-like model without ghosts
Abstract A Lee-like non-polynomial Lagrangian is discussed. The fourth order calculations in the major coupling, for the propagator function are finite but dominate over the second order terms, asymptotically. This implies that for using non-polynomial Lagrangians at high energy, one must include the higheer order terms in the major coupling. It is shown that the model has no ghosts, but does not satisfy the theorem of Lehmann, Symanzik and Zimmermann.
123113521
RECIPROCAL BOOTSTRAP OF N AND N* WITH A NONPOLYNOMIAL LAGRANGIAN.
123359231
ON THE INDEFINITE METRIC.
Abstract We point out: (i) a pseudo-hermitian Hamiltonian has conjugate-energy states if its complex eigenvalues do not belong to the residual spectrum of its adjoint, (ii) particle-antiparticle symmetry puts certain restrictions on the decay channels if there are to be no negative norm, real-energy states, and (iii) exponential time dependence of decays is valid for a pseudo-hermitian Hamiltonian if the initial conditions are chosen with care.
122034057
Ground-state energy of two-dimensional weakly coupled Hamiltonians
It is observed' that a short-range attractive potential always produces a bound state in one or two dimensions. While this property has attracted considerable attention for one-dimensional potentials, leading to many general results, ' ' much less is known about the corresponding property in two dimensions. This may be due to the fact that the bound state is marginal in the case of two dimensions, and somewhat harder to analyze. Apart from the original result of Landau and Lifshitz, ' the only other results known for the two-dimensional problem are those obtained by Simon. ' For the two-dimensional Ham iltonian verse of the T matrix, thus allowing a perturbative description of the poles of the T matrix and hence the bound-state energies. In our present note, the ground-state energy of Hmniltonian (1) is analyzed using the Noyes form' of the T matrix. We find that for potentials satisfying conditions (2) and (3), the ground-state energy has an asymptotic series given by
122539381
Nonperturbative approach to screened Coulomb potentials
The energy levels of two simple examples of screened Coulomb potentials have been analyzed using nonperturbative methods. The analysis indicates that the energy levels as a function of the perturbation parameter ) have a branch cut along the negative real axis; starting from the origin. Furthermore, there are singularities on the second sheet, along ~X~e '' for ~X ~0. As a consequence of these singularities, the energy levels have an asymptotic series in X, which means that orie cannot use a power series in X to describe the energy levels to an arbitrary accuracy, The approximate but nonperturbative expression for the energy levels, which has been obtained by using dispersion relations, predicts energy levels which are in good agreement with those obtained from variational calculations.