String duality and nonsupersymmetric strings

We present how to construct elliptically fibered K3 surfaces via Weierstrass models which can be parametrized in terms of Wilson lines in the dual heterotic string theory. We work with a subset of reflexive polyhedras that admit two fibers whose moduli spaces contain the ones of the E_{8}times E_{8} or frac{Spin(32)}{{mathbb {Z}}_{2}} heterotic theory compactified on a two torus without Wilson lines. One can then interpret the additional moduli as a particular Wilson line content in the heterotic strings. A convenient way to find such polytopes is to use graphs of polytopes where links are related to inclusion relations of moduli spaces of different fibers. We are then able to map monomials in the defining equations of particular K3 surfaces to Wilson line moduli in the dual theories. Graphs were constructed developing three different programs which give the gauge group for a generic point in the moduli space, the Weierstrass model as well as basic enhancements of the gauge group obtained by sending coefficients of the hypersurface equation defining the K3 surface to zero.

The web of dual gauge theories engineered from a class of toric Calabi-Yau threefolds is explored. In previous work, we have argued for a triality structure by compiling evidence for the fact that every such manifold XN,M (for given (N, M)) engineers three a priori different, weakly coupled quiver gauge theories in five dimensions. The strong coupling regime of the latter is in general described by Little String Theories. Furthermore, we also conjectured that the manifold XN,M is dual to XN ′,M ′ if NM = N′M′ and gcd(N, M) = gcd(N′, M′). Combining this result with the triality structure, we currently argue for a large number of dual quiver gauge theories, whose instanton partition functions can be computed explicitly as specific expansions of the topological partition function {mathcal{Z}}_{N,M} of XN,M. We illustrate this web of dual theories by studying explicit examples in detail. We also undertake first steps in further analysing the extended moduli space of XN,M with the goal of finding other dual gauge theories.

The lower limit on the age of the universe derived from globular cluster dating techniques, which previously strongly motivated a non-zero cosmological constant, has now been dramatically reduced, allowing consistency for a flat matter dominated universe with a Hubble Constant, $H_0 \le 66 km s^{-1} Mpc^{-1}$. The case for an open universe versus a flat universe with non-zero cosmological constant is reanalyzed in this context, incorporating not only the new age data, but also updates on baryon abundance constraints, and large scale structure arguments. For the first time, the allowed parameter space for the density of non-relativistic matter appears larger for an open universe than for a flat universe with cosmological constant, while a flat universe with zero cosmological constant remains strongly disfavored. Several other preliminary observations suggest a non-zero cosmological constant, but a definitive determination awaits refined measurements of $q_0$, and small scale anisotropies of the Cosmic Microwave background. I argue that fundamental theoretical arguments favor a non-zero cosmological constant over an open universe. However, if either case is confirmed, the challenges posed for fundamental particle physics will be great.

We extend our study of the large-$N$ expansion of general nonequilibrium many-body systems with matrix degrees of freedom $M$, and its dual description as a sum over surface topologies in a dual string theory, to the Keldysh-rotated version of the Schwinger-Keldysh formalism. The Keldysh rotation trades the original fields ${M}_{\ifmmode\pm\else\textpm\fi{}}$---defined as the values of $M$ on the forward and backward segments of the closed time contour---for their linear combinations ${M}_{\mathrm{cl}}$ and ${M}_{\mathrm{qu}}$, known as the ``classical'' and ``quantum'' fields. First we develop a novel ``signpost'' notation for nonequilibrium Feynman diagrams in the Keldysh-rotated form, which simplifies the analysis considerably. Before the Keldysh rotation, each world-sheet surface $\mathrm{\ensuremath{\Sigma}}$ in the dual string theory expansion was found to exhibit a triple decomposition into the parts ${\mathrm{\ensuremath{\Sigma}}}^{\ifmmode\pm\else\textpm\fi{}}$ corresponding to the forward and backward segments of the closed time contour, and ${\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{\wedge}}$ which corresponds to the instant in time where the two segments meet. After the Keldysh rotation, we find that the world-sheet surface $\mathrm{\ensuremath{\Sigma}}$ of the dual string theory undergoes a very different natural decomposition: $\mathrm{\ensuremath{\Sigma}}$ consists of a ``classical'' part ${\mathrm{\ensuremath{\Sigma}}}^{\mathrm{cl}}$ and a ``quantum embellishment'' part ${\mathrm{\ensuremath{\Sigma}}}^{\mathrm{qu}}$. We show that both parts of $\mathrm{\ensuremath{\Sigma}}$ carry their own independent genus expansion. The nonequilibrium sum over world-sheet topologies is naturally refined into a sum over the double decomposition of each $\mathrm{\ensuremath{\Sigma}}$ into its classical and quantum part. We apply this picture to the classical limits of the quantum nonequilibrium system (with or without interactions with a thermal bath), and find that in these limits, the dual string perturbation theory expansion reduces to its appropriately defined classical limit.

Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and nonsupersymmetric string vacua fills out a landscape whose features are largely unknown. It is then hoped that progress in extracting phenomenological predictions from string theory--such as correlations between gauge groups, matter representations, potential values of the cosmological constant, and so forth--can be achieved through statistical studies of these vacua. To date, most of the efforts in these directions have focused on type I vacua. In this note, we present the first results of a statistical study of the heterotic landscape, focusing on more than 10{sup 5} explicit nonsupersymmetric tachyon-free heterotic string vacua and their associated gauge groups and one-loop cosmological constants. Although this study has several important limitations, we find a number of intriguing features which may be relevant for the heterotic landscape as a whole. These features include different probabilities and correlations for different possible gauge groups as functions of the number of orbifold twists. We also find a vast degeneracy amongst nonsupersymmetric string models, leading to a severe reduction in the number of realizable values of the cosmological constant as compared with naieve expectations. Finally, we find strong correlations between cosmological constantsmore » and gauge groups which suggest that heterotic string models with extremely small cosmological constants are overwhelmingly more likely to exhibit the standard model gauge group at the string scale than any of its grand-unified extensions. In all cases, heterotic world sheet symmetries such as modular invariance provide important constraints that do not appear in corresponding studies of type I vacua.« less

Strong/weak coupling duality relations for non-supersymmetric string theories

The Sachdev-Ye-Kitaev (SYK) model is a quantum mechanical many body system with random all-to-all interactions on fermionic N sites (N>>1). This model is shown to saturate the known maximal chaos bound of many body system and then based on this observation it is conjectured to be dual to a quantum black hole in the sense of the AdS/CFT correspondence. In this dissertation, we show that the large N physics of the SYK model is systematically described by a single bi-local field. In particular, we emphasize the appearance of the emergent conformal reparametrization symmetry at the critical IR fixed point and the corresponding divergent contribution of the symmetry modes in the propagator of the bi-local field. We discuss non-linear-level derivation of the zero modes effective action, which is given by the Schwarzian derivative for finite reparametrization symmetry. Besides the symmetry modes, which correspond to the dilaton-gravity sector in the dual AdS theory, the SYK model also predicts an infinite tower of matter fields in AdS_2. We demonstrate that this infinite spectrum can be nicely packaged into a single field in 3-dimensional space-time. Finally, we consider the question of identifying the dual space-time of the SYK model. Focusing on the signature of emergent space-time of the (Euclidean) model, we explain the need for non-local (Radon-type) transformations on external legs of n-point Green's functions. This results in a dual theory with Euclidean AdS signature with additional leg-factors. We speculate that these factors incorporate the coupling of additional bulk states similar to the discrete states of 2D string theory.

We investigate backgrounds of Type IIB string theory with null singularities and their duals proposed in S. R. Das, J. Michelson, K. Narayan, S. P. Trivedi, hep-th/0602107. The dual theory is a deformed $\mathcal{N}=4$ Yang-Mills theory in $3+1$ dimensions with couplings dependent on a lightlike direction. We concentrate on backgrounds which become ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ at early and late times and where the string coupling is bounded, vanishing at the singularity. Our main conclusion is that in these cases the dual gauge theory is nonsingular. We show this by arguing that there exists a complete set of gauge invariant observables in the dual gauge theory whose correlation functions are nonsingular at all times. The two-point correlator for some operators calculated in the gauge theory does not agree with the result from the bulk supergravity solution. However, the bulk calculation is invalid near the singularity where corrections to the supergravity approximation become important. We also obtain pp-waves which are suitable Penrose limits of this general class of solutions, and construct the matrix membrane theory which describes these pp-wave backgrounds.

Static vacuum near horizon geometries are solutions $(M,g,X)$ of a certain quasi-Einstein equation on a closed manifold $M$, where $g$ is a Riemannian metric and $X$ is a closed 1-form. It is known that when the cosmological constant vanishes, there is rigidity: $X$ vanishes and consequently $g$ is Ricci flat. We study this form of rigidity for all signs of the cosmological constant. It has been asserted that this rigidity also holds when the cosmological constant is negative, but we exhibit a counter-example. We show that for negative cosmological constant if $X$ does not vanish identically, it must be incompressible, have constant norm, and be nontrivial in cohomology, and $(M,g)$ must have constant scalar curvature and zero Euler characteristic. If the cosmological constant is positive, $X$ must be exact (and vanishing if $\dim M=2$). Our results apply more generally to a broad class of quasi-Einstein equations on closed manifolds. We extend some known results for quasi-Einstein metrics with exact 1-form $X$ to the closed $X$ case. We consider near horizon geometries for which the vacuum condition is relaxed somewhat to allow for the presence of a limited class of matter fields. An appendix contains a generalization of a result of Lucietti on the Yamabe type of quasi-Einstein compact metrics (with arbitrary $X$).

The cosmological constant and domain walls in orientifold field theories and [formula omitted] gluodynamics

A pedagogical treatment to the effect of cosmological constant in the big-bang model is presented. It is argued that quantum fluctuations of the vacuum contributes to the cosmological constant and, essentially, leads to the cosmological constant problem. The equation of state corresponding to the cosmological constant is derived using the conservation of energy-momentum tensor in the Friedman models. The epoch after which the cosmological constant starts dominating over the non-relativistic matter is calculated. The evolution of the expansion factor as a function of cosmic time is discussed for the flat model case when A is positive. The ensuing age of the universe since the birth of high redshift QSOs is compared with the ages of the globular clusters. Collapse of a spherical dust ball and its virialization is considered. The flatness problem in the presence of a non-zero cosmological constant is discussed.

In an attempt to reconcile the large number hypothesis (LNH) with Einstein's theory of gravitation, a tentative generalization of Einstein's field equations with time-dependent cosmological and gravitational constants is proposed. A cosmological model consistent with the LNH is deduced. The coupling formula of the cosmological constant with matter is found, and as a consequence, the time-dependent formulae of the cosmological constant and the mean matter density of the Universe at the present epoch are then found. Einstein's theory of gravitation, whether with a zero or nonzero cosmological constant, becomes a limiting case of the new generalized field equations after the early epoch.

In this paper we study about the M−projectively flat perfect fluid spacetime. First of all we showed that the Riemannian curvature tensor of an M−projectively flat spacetime is covariantly constant. Then we found the length of the Ricci operator in an M−projectively flat perfect fluid spacetime and proved that the isotropic pressure and entry density of an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant are constant. Then we showed that an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant and obeying the timelike convergence condition has positive isotropic pressure. Further we showed that the isotropic pressure and the energy density of an M−projectively flat perfect fluid spacetime satisfying Einsteins field equation with cosmological constant vanishes in a purely electromagnetic distribution. Lastly we showed that an M−projectively flat perfect fluid spacetime with the energy momentum tensor of an electromagnetic field such that the spacetimesatisfies Einsteins field equation without cosmological constant is a Euclidean space

The quantization of Einstein-Maxwell theory with a cosmological constant is considered. We obtain all logarithmically divergent terms in the one-loop effective action that involve only the background electromagnetic field. This includes Lee-Wick--type terms, as well as those responsible for the renormalization group behavior of the electric charge (or fine structure constant). Of particular interest is the possible gauge condition dependence of the results, and we study this in some detail. We show that the traditional background-field method, that is equivalent to a more traditional Feynman diagram calculation, does result in gauge condition dependent results in general. One resolution of this is to use the Vilkovisky-DeWitt effective action method, and this is presented here. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This reopens the possibility, suggested by Robinson and Wilczek, of altering the scaling behavior of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.

The quantum gravitational contribution to the renormalization group behavior of the electric charge in Einstein-Maxwell theory with a cosmological constant is considered. Quantum gravity is shown to lead to a contribution to the running charge not present when the cosmological constant vanishes. This reopens the possibility, suggested by Robinson and Wilczek, of altering the scaling behavior of gauge theories at high energies although our result differs. We show the possibility of an ultraviolet fixed point that is linked directly to the cosmological constant.