Large Volume Limit Research Articles

A model for enhanced and selective transport through biological membranes with alternating pores

We investigate the outflux of ions through the channels in a cell membrane. The channels undergo an open/close cycle according to a periodic schedule. Our study is based both on theoretical considerations relying on homogenization theory, and on Monte Carlo numerical simulations. We examine the onset of a limiting boundary behavior characterized by a constant ratio between the outflux and the local density, in the large volume limit. The focus here is on the issue of selectivity, that is on the different behavior of the ion currents through the channel in the cases of the selected and non-selected species.

Calabi’s diastasis as interface entropy

We show that the entropy of certain conformal interfaces between $N=(2,2)$ sigma models that belong to the same moduli space, has a natural geometric interpretation in the large volume limit as Calabi's diastasis function. This is an extension of the well-known relation between the quantum K\"ahler potential and the overlap of canonical Ramond-Ramond ground states in $N=(2,2)$ models.

Dynamics of warped flux compactifications with backreacting antibranes

We revisit the effective low-energy dynamics of the volume modulus in warped flux compactifications with anti-D3-branes in order to analyze the prospects for metastable de Sitter vacua and brane inflation along the lines of KKLT/KKLMMT. At the level of the ten-dimensional supergravity solution, antibranes in flux backgrounds with opposite charge are known to source singular terms in the energy densities of the bulk fluxes, which led to a debate on the consistency of such constructions in string theory. A straightforward yet nontrivial check of the singular solution is to verify that its dimensional reduction in the large-volume limit reproduces the four-dimensional low-energy dynamics expected from known results where the antibranes are treated as a probe. Taking into account the antibrane backreaction in the effective scalar potential, we find that both the volume scaling and the coefficient of the antibrane uplift term are in exact agreement with the probe potential if the singular fluxes satisfy a certain near-brane boundary condition. This condition can be tested explicitly and may thus help to decide whether flux singularities should be interpreted as pathological or benign features of flux compactifications with antibranes. Throughout the paper, we also comment on a number of subtleties related to the proper definition of warped effective field theory with antibranes.

The exact solution of a mean-field monomer-dimer model with attractive potential

A monomer-dimer model with an attractive interaction that favors a phase separation between monomers and dimers is exactly solved in the mean-field case. With the identification of a suitable variational principle the free energy is computed in the large volume limit using the Heilmann-Lieb pure hard-core ansatz. The monomer density, that turns out to be the order parameter of the model, is shown to have a first-order phase transition along a coexistence curve.

The large-volume limit of a quantum tetrahedron is a quantum harmonic oscillator

It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.

The dimensional reduction and Kähler metric of forms in flux and warping

We present a first-principles derivation of the Kähler metric for axion-like moduli of conformally Calabi-Yau compactifications of IIB string theory with imaginary self-dual 3-form flux at the classical level. We find that the warp factor and flux modify the moduli space metric and therefore Kähler potential even in classical supergravity, with the modifications scaling as (volume)−2/3 in the large-volume limit. Our derivation emphasizes the role of constraints from 10D gauge symmetries and highlights metric formality as a geometric property that protects the moduli space of highly supersymmetric toroidal orientifolds. Our results have important quantitative implications for nonperturbative moduli stabilization, phenomenology, and cosmology in flux compactifications.

Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities

We construct new t-structures on the derived category of coherent sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the large volume limit. We show that this conjecture is equivalent to a Bogomolov-Gieseker type inequality for the third Chern character of certain stable complexes. We also conjecture a stronger inequality, and prove it in the case of projective space, and for various examples.Finally, we prove a version of the classical Bogomolov-Gieseker inequality, not involving the third Chern character, for stable complexes.

Large-Ncgauge theory and chiral random matrix theory

We discuss how the $1/{N}_{c}$ expansion and the chiral random matrix theory ($\ensuremath{\chi}\mathrm{RMT}$) can be used in the study of large-${N}_{c}$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid. While the fermion mass $m$ is fixed in the standard large-${N}_{c}$ arguments ('t Hooft large-${N}_{c}$ limit), $m$ must be scaled appropriately with a certain negative power of ${N}_{c}$ in order for the gauge theories to be described by the $\ensuremath{\chi}\mathrm{RMT}$. Then, although these two limits are not compatible in general, we show that the breakdown of chiral symmetry can be detected by combining the large-${N}_{c}$ argument and the $\ensuremath{\chi}\mathrm{RMT}$ with some care. As a concrete example, we numerically study the four-dimensional $SU({N}_{c})$ gauge theory with ${N}_{f}=2$ heavy adjoint fermions, introduced as the center symmetry preserver keeping the infrared physics intact, on a ${2}^{4}$ lattice. By looking at the low-lying eigenvalues of the overlap-Dirac operator for a massless probe fermion in the adjoint representation, we find that the chiral symmetry is indeed broken with the expected breaking pattern. This result reproduces a well-known fact that the chiral symmetry is spontaneously broken in the pure $SU({N}_{c})$ gauge theory in the large-${N}_{c}$ and the large-volume limit and therefore supports the validity of the combined approach. We also provide an interpretation of the gap and unexpected ${N}_{c}$ scaling, both of which are observed in the Dirac spectrum.

Gluing branes — II: flavour physics and string duality

Recently we discussed new aspects of degenerate brane configurations, which can appear in the context of heterotic strings, perturbative type II, or M/F-theory. Here we continue our study of degenerate brane configurations, focussing on two applications. First we show how the notion of gluing can be viewed as a tool to engineer flavour structures in F-theory and type IIb, such as models with bulk matter and with Yukawa textures arising from the holomorphic zero mechanism. We find that there is in principle enough structure to solve some of the major flavour problems without generating exotics. In particular, we show how this addresses the μ-problem, doublet/triplet splitting and proton decay. Secondly, we describe the Fourier-Mukai transform of heterotic monad constructions, which occur in the large volume limit of heterotic linear sigma model vacua. Degenerate structures again often appear. One may use this to explore strong coupling phenomena using heterotic/F-theory duality.

Dynamical eigenfunctions and critical density in loop quantum cosmology

We offer a new, physically transparent argument for the existence of the critical, universal maximum matter density in loop quantum cosmology for the case of a flat Friedmann–Lemaître–Robertson–Walker cosmology with scalar matter. The argument is based on the existence of a sharp exponential ultraviolet cutoff in momentum space on the eigenfunctions of the quantum cosmological dynamical evolution operator (the gravitational part of the Hamiltonian constraint), attributable to the fundamental discreteness of spatial volume in loop quantum cosmology. The existence of the cutoff is proved directly from recently found exact solutions for the eigenfunctions for this model. As a consequence, the operators corresponding to the momentum of the scalar field and the spatial volume approximately commute. The ultraviolet cutoff then implies that the scalar momentum, though not a bounded operator, is in effect bounded on subspaces of constant volume, leading to the upper bound on the expectation value of the matter density. The maximum matter density is universal (i.e. independent of the quantum state) because of the linear scaling of the cutoff with volume. These heuristic arguments are supplemented by a new proof in the volume representation of the existence of the maximum matter density. The techniques employed to demonstrate the existence of the cutoff also allow us to extract the large-volume limit of the exact eigenfunctions, confirming earlier numerical and analytical work showing that the eigenfunctions approach superpositions of the eigenfunctions of the Wheeler–DeWitt quantization of the same model. We argue that generic (not just semiclassical) quantum states approach symmetric superpositions of expanding and contracting universes.

Geodesics on Calabi-Yau manifolds and winding states in non-linear sigma models

We conjecture that a non-flat $D$-real-dimensional compact Calabi-Yau manifold, such as a quintic hypersurface with D=6, or a K3 manifold with D=4, has locally length minimizing closed geodesics, and that the number of these with length less than L grows asymptotically as L^{D}. We also outline the physical arguments behind this conjecture, which involve the claim that all states in a nonlinear sigma model can be identified as "momentum" and "winding" states in the large volume limit.

Necessary conditions on Calabi-Yau manifolds for large volume vacua

We describe an efficient, construction independent, algorithmic test to determine whether Calabi-Yau threefolds admit a structure compatible with the large volume moduli stabilization scenario of type IIB superstring theory. Using the algorithm, we scan complete intersection and toric hypersurface Calabi-Yau threefolds with $2\ensuremath{\le}{h}^{1,1}\ensuremath{\le}4$ and deduce that 418 among 4434 manifolds have a large volume limit with a single large four-cycle. We describe major extensions to this survey, which are currently underway.

Building an explicit de Sitter

Abstract We construct an explicit example of a de Sitter vacuum in type IIB string theory that realizes the proposal of Kähler uplifting. As the large volume limit in this method depends on the rank of the largest condensing gauge group we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric Calabi-Yau threefolds. We find large numbers of models with the largest gauge group factor easily exceeding a rank of one hundred. We construct a global model with Kähler uplifting on a two-parameter model on $ \mathbb{CP}_{11169}^4 $ , by an explicit analysis from both the type IIB and F-theory point of view. The explicitness of the construction lies in the realization of a D7 brane configuration, gauge flux and RR and NS flux choices, such that all known consistency conditions are met and the geometric moduli are stabilized in a metastable de Sitter vacuum with spontaneous GUT scale supersymmetry breaking driven by an F-term of the Kähler moduli.

Structure in 6D and 4D $ \mathcal{N}=1 $ supergravity theories from F-theory

We explore some aspects of 4D supergravity theories and F-theory vacua that are parallel to structures in the space of 6D theories. The spectrum and topological terms in 4D supergravity theories correspond to topological data of F-theory geometry, just as in six dimensions. In particular, topological axion-curvature squared couplings appear in 4D theories; these couplings are characterized by vectors in the dual to the lattice of axion shift symmetries associated with string charges. These terms are analogous to the Green-Schwarz terms of 6D supergravity theories, though in 4D the terms are not generally linked with anomalies. We outline the correspondence between F-theory topology and data of the corresponding 4D supergravity theories. The correspondence of geometry with structure in the low-energy action illuminates topological aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of an F-theory realization also places geometrical constraints on the 4D supergravity theory in the large-volume limit.

A Matrix Model for the Topological String II: The Spectral Curve and Mirror Geometry

In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing certain minimality assumptions on the spectral curve, the large volume limit of the BKMP "remodeling the B-model" conjecture, the claim that Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the spectral invariants of its mirror curve.

LOCAL D3/D7 μ-SPLIT SUSY, 125 GeV HIGGS AND LARGE VOLUME RICCI-FLAT SWISS-CHEESE METRICS: A BRIEF REVIEW

In this paper, we review briefly recent progress made in realizing local(ized around a mobile spacetime filling D3-brane in) D3/D7 μ-split Supersymmetry in (the large volume limit of Type IIB) String Theory (compactified on Swiss-Cheese Calabi–Yau orientifolds) as well as obtaining a 125 GeV (light) Higgs in the same setup. We also discuss obtaining the geometric Kähler potential (and hence the Ricci-flat metric) for the Swiss-Cheese Calabi–Yau in the large volume limit using the Donaldson's algorithm and intuition from GLSM-based calculations — we present new results for Swiss-Cheese Calabi–Yau (used in the setup) metrics at points finitely away from the "big" divisor.

Colored Tensor Models - a Review

Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions), non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.

Many-node/many-link spinfoam: the homogeneous and isotropic case

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude at the first order for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the complete graph on five nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large-j (large-volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit, quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large-j limit.

Split states, entropy enigmas, holes and halos

We investigate degeneracies of BPS states of D-branes on compact Calabi-Yau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial D-brane systems, and to clarify the subtle relation of Donaldson-Thomas invariants to BPS indices of stable D6-D2-D0 states, realized in supergravity as "hole halos". We introduce a convergent generating function for D4 indices in the large CY volume limit, and prove it can be written as a modular average of its polar part, generalizing the fareytail expansion of the elliptic genus. We show polar states are "split" D6-anti-D6 bound states, and that the partition function factorizes accordingly, leading to a refined version of the OSV conjecture. This differs from the original conjecture in several aspects. In particular we obtain a nontrivial measure factor g_{top}^{-2} e^{-K} and find factorization requires a cutoff. We show that the main factor determining the cutoff and therefore the error is the existence of "swing states" -- D6 states which exist at large radius but do not form stable D6-anti-D6 bound states. We point out a likely breakdown of the OSV conjecture at small g_{top} (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kahler moduli, a charge N Q supporting single centered black holes of entropy ~ N^2 S(Q) also admits two-centered BPS black hole realizations whose entropy grows like N^3 at large N.

Towards large volume big divisor D3/D7 “ μ-split supersymmetry” and Ricci-flat Swiss-cheese metrics, and dimension-six neutrino mass operators

We show that it is possible to realize a “ μ-split SUSY” scenario (Cheng and Cheng, 2005) [1] in the context of large volume limit of type IIB compactifications on Swiss-cheese Calabi–Yau orientifolds in the presence of a mobile space–time filling D3-brane and a (stack of) D7-brane(s) wrapping the “big” divisor. For this, we investigate the possibility of getting one Higgs to be light while other to be heavy in addition to a heavy higgsino mass parameter. Further, we examine the existence of long lived gluino that manifests one of the major consequences of μ-split SUSY scenario, by computing its decay width as well as lifetime corresponding to the three-body decays of the gluino into either a quark, a squark and a neutralino or a quark, squark and goldstino, as well as two-body decays of the gluino into either a neutralino and a gluon or a goldstino and a gluon. Guided by the geometric Kähler potential for Σ B obtained in Misra and Shukla (2010) [2] based on GLSM techniques, and the Donaldsonʼs algorithm (Barun et al., 2008) [3] for obtaining numerically a Ricci-flat metric, we give details of our calculation in Misra and Shukla (2011) [4] pertaining to our proposed metric for the full Swiss-cheese Calabi–Yau (the geometric Kähler potential being needed to be included in the full moduli space Kähler potential in the presence of the mobile space–time filling D3-brane), but for simplicity of calculation, close to the big divisor, which is Ricci-flat in the large volume limit. Also, as an application of the one-loop RG flow solution for the higgsino mass parameter, we show that the contribution to the neutrino masses at the EW scale from dimension-six operators arising from the Kähler potential, is suppressed relative to the Weinberg-type dimension-five operators.