Large Volume Limit Research Articles

A 2D model of causal set quantum gravity: the emergence of the continuum

Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining the desired classical limit. We examine this ‘entropy problem’ in a model of causal set quantum gravity corresponding to a discretization of 2D spacetimes. Using results from the theory of partial orders we show that, in the large volume or continuum limit, its partition function is dominated by causal sets which approximate to a region of 2D Minkowski space. This model of causal set quantum gravity thus overcomes the entropy problem and predicts the emergence of a physically reasonable geometry.

Large volume axionic Swiss cheese inflation

Continuing with the ideas of (Section 4 of) [A. Misra, P. Shukla, Moduli stabilization, large-volume dS minimum without anti-D3-branes, (non-)supersymmetric black hole attractors and two-parameter Swiss cheese Calabi–Yau's, arXiv: 0707.0105 [hep-th], Nucl. Phys. B, in press], after inclusion of perturbative and non-perturbative α ′ corrections to the Kähler potential and (D1- and D3-) instanton generated superpotential, we show the possibility of slow roll axionic inflation in the large volume limit of Swiss cheese Calabi–Yau orientifold compactifications of type IIB string theory. We also include one- and two-loop corrections to the Kähler potential but find the same to be subdominant to the (perturbative and non-perturbative) α ′ corrections. The NS–NS axions provide a flat direction for slow roll inflation to proceed from a saddle point to the nearest dS minimum.

Multiplicity fluctuations in limited segments of momentum space in statistical models

Multiplicity fluctuations in limited segments of momentum space are calculated for a classical pion gas within the statistical model. Results for the grand canonical, canonical, and micro-canonical ensemble are obtained, compared, and discussed. We demonstrate that even in the large volume limit correlations between macroscopic subsystems due to energy and momentum conservation persist. Based on the microcanonical formulation we make qualitative predictions for the rapidity and transverse-momentum dependence of multiplicity fluctuations. The resulting effects are of similar magnitude as the predicted enhancement due to a phase transition from a quark-gluon plasma to a hadron gas phase or due to the critical point of strongly interacting matter and qualitatively agree with recently published preliminary multiplicity fluctuation data of the NA49 SPS experiment.

Multiplicity fluctuations in relativistic nuclear collisions: statistical model versus experimental data

Multiplicity distributions of hadrons produced in central nucleus–nucleus collisions are studied within the hadron-resonance gas model in the large volume limit. In the canonical ensemble conservation of three charges (baryon number, electric charge and strangeness) is enforced. In addition, in the micro-canonical ensemble, energy conservation is included. An analytical method is used to account for resonance decays. Multiplicity distributions and scaled variances for negatively charged hadrons are presented along the chemical freeze-out line of central Pb+Pb (Au+Au) collisions from SIS to LHC energies. Predictions obtained within different statistical ensembles are compared with preliminary NA49 experimental results on central Pb+Pb collisions in the SPS energy range. The measured fluctuations are significantly narrower than a Poisson reference distribution, and clearly favor expectations for the micro-canonical ensemble.

NLIE of Dirichlet sine-Gordon model for boundary bound states

We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Lüscher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory.

On phases of generic toric singularities

We systematically study the phases of generic toric singularities, using methods initiated in hep-th/0612046. These correspond to large volume limits of certain Gauged Linear Sigma Models. We show that complete information about the classical regimes of generic U(1)r GLSMs can be obtained by studying the GLSM Lagrangian, appropriately modified in the different phases of the theory. We use this to study some aspects of La,b,c spaces and their non-supersymmetric counterparts.

Non-perturbative corrections and modularity in 𝒩 = 1 type IIB compactifications

Non-perturbative corrections and modular properties of four-dimensional type IIB Calabi-Yau orientifolds are discussed. It is shown that certain non-perturbative alpha' corrections survive in the large volume limit of the orientifold and periodically correct the Kahler potential. These corrections depend on the NS-NS two form and have to be completed by D-instanton contributions to transform covariantely under symmetries of the type IIB orientifold background. It is shown that generically also the D-instanton superpotential depends on the two-form moduli as well as on the complex dilaton. These contributions can arise through theta-functions with the dilaton as modular parameter. An orientifold of the Enriques Calabi-Yau allows to illustrate these general considerations. It is shown that this compactification leads to a controlled four-dimensional N=1 effective theory due to the absence of various quantum corrections. Making contact to the underlying topological string theory the D-instanton superpotential is proposed to be related to a specific modular form counting D3, D1, D(-1) degeneracies on the Enriques Calabi-Yau.

Jumping through loops: on soft terms from large volume compactifications

We subject the phenomenologically successful large volume scenario of hep-th/0502058 to a first consistency check in string theory. In particular, we consider whether the expansion of the string effective action is consistent in the presence of D-branes and O-planes. Due to the no-scale structure at tree-level, the scenario is surprisingly robust. We compute the modification of soft supersymmetry breaking terms, and find only subleading corrections. We also comment that for large-volume limits of toroidal orientifolds and fibered Calabi-Yau manifolds the corrections can be more important, and we discuss further checks that need to be performed.

Fitting two nucleons inside a box: Exponentially suppressed corrections to Lüscher’s formula

Scattering observables can be computed in lattice field theory by measuring the volume dependence of energy levels of two-particle states. The dominant volume dependence, proportional to inverse powers of the volume, is determined by the phase shifts. This universal relation (L\"uscher's formula) between energy levels and phase shifts is distorted by corrections which, in the large volume limit, are exponentially suppressed. They may be sizable, however, for the volumes used in practice, and they set a limit on how small the lattice can be in these studies. We estimate these corrections, mostly in the case of two nucleons. Qualitatively, we find that the exponentially suppressed corrections are proportional to the square of the potential (or to terms suppressed in the chiral expansion) and the effect due to pions going ``around the world'' vanishes. Quantitatively, the size of the lattice should be greater than $\ensuremath{\approx}(5\text{ }\text{ }\mathrm{fm}{)}^{3}$ in order to keep finite volume corrections to the phase less than 1\ifmmode^\circ\else\textdegree\fi{} for realistic pion mass.

Multiplicity fluctuations in relativistic nuclear collisions: Statistical model versus experimental data

The multiplicity distributions of hadrons produced in central nucleus-nucleus collisions are studied within the hadron-resonance gas model in the large-volume limit. The microscopic correlator method is used to enforce conservation of three charges---baryon number, electric charge, and strangeness---in the canonical ensemble. In addition, in the microcanonical ensemble energy conservation is included. An analytical method is used to account for resonance decays. The multiplicity distributions and the scaled variances for negatively, positively, and all charged hadrons are calculated along the chemical freeze-out line of central $\mathrm{Pb}+\mathrm{Pb}$ ($\mathrm{Au}+\mathrm{Au}$) collisions from GSI Schwerionen Synchrotron to CERN Large Hadron Collider energies. Predictions obtained within different statistical ensembles are compared with the preliminary NA49 experimental results on central $\mathrm{Pb}+\mathrm{Pb}$ collisions in the SPS energy range. The measured fluctuations are significantly narrower than the Poisson ones and clearly favor expectations for the microcanonical ensemble. Thus this is the first observation of the recently predicted suppression of the multiplicity fluctuations in relativistic gases in the thermodynamical limit owing to conservation laws.

A scan for new Script N = 1 vacua on twisted tori

We perform a systematic search for N=1 Minkowski vacua of type II string theories on compact six-dimensional parallelizable nil- and solvmanifolds (quotients of six-dimensional nilpotent and solvable groups, respectively). Some of these manifolds have appeared in the construction of string backgrounds and are typically called twisted tori. We look for vacua directly in ten dimensions, using the a reformulation of the supersymmetry condition in the framework of generalized complex geometry. Certain algebraic criteria to establish compactness of the manifolds involved are also needed. Although the conditions for preserved N=1 supersymmetry fit nicely in the framework of generalized complex geometry, they are notoriously hard to solve when coupled to the Bianchi identities. We find solutions in a large-volume, constant-dilaton limit. Among these, we identify those that are T-dual to backgrounds of IIB on a conformal T^6 with self-dual three-form flux, and hence conceptually not new. For all backgrounds of this type fully localized solutions can be obtained. The other new solutions need multiple intersecting sources (either orientifold planes or combinations of O-planes and D-branes) to satisfy the Bianchi identities; the full list of such new solution is given. These are so far only smeared solutions, and their localization is yet unknown. Although valid in a large-volume limit, they are the first examples of Minkowski vacua in supergravity which are not connected by any duality to a Calabi-Yau. Finally, we discuss a class of flat solvmanifolds that may lead to AdS_4 vacua of type IIA strings.

A second order deconfinement transition for largeN2+1 dimensional Yang-Mills theory on a smallS2

We study the thermodynamics of large N pure 2+1 dimensional Yang-Mills theory on a small spatial sphere. By studying the effective action for the Polyakov loop order parameter, we show analytically that the theory has a second order deconfinement transition to a phase where the eigenvalue distribution of the Polyakov loop is non-uniform but still spread over the whole unit circle. At a higher temperature, the eigenvalue distribution develops a gap, via an additional third-order phase transition. We discuss possible forms of the full phase diagram as a function of temperature and sphere radius. Our results together with extrapolation of lattice results relevant to the large volume limit imply the existence of a critical radius in the phase diagram at which the deconfinement transition switches from second order to first order. We show that the point at the critical radius and temperature can be either a tricritical point with universal behavior or a triple point separating three distinct phases.

Loop quantum cosmology and the Wheeler–De Witt equation

We present some results concerning the large volume limit of loop quantum cosmology in the flat homogeneous and isotropic case. We derive the Wheeler–De Witt equation in this limit. Looking for the action from which this equation can also be obtained, we then address the problem of the modifications to be brought to the Friedman’s equation and to the equation of motion of the scalar field, in the classical limit.

Systematics of moduli stabilization, inflationary dynamics and power spectrum

We study the scalar sector of type IIB superstring theory compactified on Calabi-Yau orientifolds as a place to find a mechanism of inflation in the early universe. In the large volume limit, one can stabilize the moduli in stages using perturbative method. We relate the systematics of moduli stabilization with methods to reduce the number of possible inflatons, which in turn lead to a simpler inflation analysis. Calculating the order-of-magnitude of terms in the equation of motion, we show that the methods are in fact valid. We then give the examples where these methods are used in the literature. We also show that there are effects of non-inflaton scalar fields on the scalar power spectrum. For one of the two methods, these effects can be observed with the current precision in experiments, while for the other method, the effects might never be observable.

On a projection in dependence on monopole condensate in the lattice SU(2) gauge theory

We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) lattice gauge theory in the thermodynamic limit. Using the Fröhlich-Marchetti monopole creation operator, we show numerically that the monopole condensate depends strongly on the choice of the Abelian projection. Contrary to the claims in the literature, we observe that, in the Abelian-Polyakov gauge and in the field strength gauge, the monopole condensate does not vanish at the critical temperature in the large-volume limit. Therefore, the monopole condensate in these gauges is not an order parameter of the confinement-deconfinement phase transition.

Infrared behavior of gluon and ghost propagators from asymmetric lattices

We present a numerical study of the lattice Landau gluon and ghost propagators in three-dimensional pure SU(2) gauge theory. Data have been obtained using asymmetric lattices (V = 20^2 X 40, 20^2 X 60, 8^2 X 64, 8^2 X 140, 12^2 X 140 and 16^2 X 140) for the lattice coupling beta = 3.4, in the scaling region. We find that the gluon (respectively ghost) propagator is suppressed (respec. enhanced) at small momenta in the limit of large lattice volume V. By comparing these results with data obtained using symmetric lattices (V = 60^3 and 140^3), we find that both propagators suffer from systematic effects in the infrared region (p \lesssim 650 MeV). In particular, the gluon (respec. ghost) propagator is less IR-suppressed (respec. enhanced) than in the symmetric case. We discuss possible implications of the use of asymmetric lattices.

From simple to complex networks: Inherent structures, barriers, and valleys in the context of spin glasses

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity N(s) of the inherent structures generically has a log-normal distribution. In addition, the large volume limit of ln <N(s)>/<ln N(s)> differs from unity, except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.

On the critical end point of QCD

We investigate the critical end point of QCD with two flavours of light dynamical quarks at finite lattice cutoff $a=1/4T$ using a Taylor expansion of the baryon number susceptibility. We find a strong volume dependence of its radius of convergence. In the large volume limit we obtain ${\ensuremath{\mu}}_{B}/T\ensuremath{\approx}1.1$ as the radius of convergence at $T/{T}_{c}\ensuremath{\approx}0.95$ where ${T}_{c}$ is the crossover temperature at zero chemical potential. Since this estimate is a lower bound on the critical end point of QCD, the above small value of $\ensuremath{\mu}$ may place it in the range of observability in energy scans at the Relativistic Heavy-Ion Collider (RHIC).

Systematics of Moduli Stabilisation in Calabi-Yau Flux Compactifications

We study the large volume limit of the scalar potential in Calabi-Yau flux compactifications of type IIB string theory. Under general circumstances there exists a limit in which the potential approaches zero from below, with an associated non-supersymmetric AdS minimum at exponentially large volume. Both this and its de Sitter uplift are tachyon-free, thereby fixing all Kahler and complex structure moduli, which has been difficult to achieve in the KKLT scenario. Also, for the class of vacua described in this paper, the gravitino mass is independent of the flux discretuum, whereas the ratio of the string scale to the 4d Planck scale is hierarchically small but flux dependent. The inclusion of alpha' corrections plays a crucial role in the structure of the potential. We illustrate these ideas through explicit computations for a particular Calabi-Yau manifold.