Sigma Model Perturbation Theory Research Articles

W-symmetries, anomalies and heterotic backgrounds with non-compact holonomy

We determine the algebra of holonomy symmetries of sigma models propagating on supersymmetric heterotic backgrounds with a non-compact holonomy group. We demonstrate that these close as a W-algebra, which in turn is specified by a Lie algebra structure on the space of covariantly constant forms that generate the holonomy symmetries. In addition, we identify the chiral anomalies associated with these symmetries. We argue that these anomalies are consistent and can be cancelled up to two loops in the sigma model perturbation theory.

W-symmetries, anomalies and heterotic backgrounds with SU holonomy

We show that the sigma models with target spaces supersymmetric heterotic backgrounds with SU(2) and SU(3) holonomy are invariant under a W-symmetry algebra generated by the covariantly constant forms of these backgrounds. The closure of the W-algebra requires additional generators that we identify. We prove that the chiral anomalies of all these symmetries are consistent at one-loop in perturbation theory. We also demonstrate that these anomalies cancel at the same loop level either by adding suitable finite local counterterms in the sigma model effective action or by assuming a plausible quantum correction to the transformations. Such a correction is compatible with both the cancellation mechanism for spacetime frame rotation and gauge transformation anomalies, and the correction to the heterotic supergravity up to two loops in the sigma model perturbation theory.

Anomaly corrected heterotic horizons

We consider supersymmetric near-horizon geometries in heterotic supergravity up to two loop order in sigma model perturbation theory. We identify the conditions for the horizons to admit enhancement of supersymmetry. We show that solutions which undergo supersymmetry enhancement exhibit an sl(2,R) symmetry, and we describe the geometry of their horizon sections. We also prove a modified Lichnerowicz type theorem, incorporating $\alpha'$ corrections, which relates Killing spinors to zero modes of near-horizon Dirac operators. Furthermore, we demonstrate that there are no AdS2 solutions in heterotic supergravity up to second order in $\alpha'$ for which the fields are smooth and the internal space is smooth and compact without boundary. We investigate a class of nearly supersymmetric horizons, for which the gravitino Killing spinor equation is satisfied on the spatial cross sections but not the dilatino one, and present a description of their geometry.

Geometry and supersymmetry of heterotic warped flux AdS backgrounds

Abstract We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no AdS n backgrounds with n ≠ 3. Moreover the warp factor of AdS3 backgrounds is constant, the geometry is a product AdS 3 × M 7 and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of M 7 has been specified in all cases. For 2 supersymmetries, it has been found that M 7 admits a suitably restricted G 2 structure. For 4 supersymmetries, M 7 has an SU(3) structure and can be described locally as a circle fibration over a 6-dimensional KT manifold. For 6 and 8 supersymmetries, M 7 has an SU(2) structure and can be described locally as a S 3 fibration over a 4-dimensional manifold which either has an anti-self dual Weyl tensor or a hyper-Kähler structure, respectively. We also demonstrate a new Lichnerowicz type theorem in the presence of α′ corrections.

High-gradient operators in the [formula omitted] Gross–Neveu model

It has been observed more than 25 years ago that sigma model perturbation theory suffers from strongly RG-relevant high-gradient operators. The phenomenon was first seen in 1-loop calculations for the O(N) vector model and it is known to persist at least to two loops. More recently, Ryu et al. suggested that a certain deformation of the psl(N|N) WZNW-model at level k=1, or equivalently the psl(N|N) Gross–Neveu model, could be free of RG-relevant high-gradient operators and they tested their suggestion to leading order in perturbation theory. In this note we establish the absence of strongly RG-relevant high-gradient operators in the psl(2|2) Gross–Neveu model to all loops. In addition, we determine the spectrum for a large subsector of the model at infinite coupling and observe that all scaling weights become half-integer. Evidence for a conjectured relation with the CP1|2 sigma model is not found.

The generalized cusp in and more one-loop results from semiclassical strings

We evaluate the exact one-loop partition function for fundamental strings whose world surface ends on a cusp at the boundary of AdS4 and has a ‘jump’ in . This allows us to extract the stringy prediction for the ABJM-generalized cusp anomalous dimension ΓABJMcusp(ϕ, θ) up to NLO in sigma-model perturbation theory. With a similar analysis, we present the exact partition functions for folded closed string solutions moving in the AdS3 parts of and AdS3 × S3 × S3 × S1 backgrounds. Results are obtained applying to the string solutions relevant for the AdS4/CFT3 and AdS3/CFT2 correspondence the tools previously developed for their AdS5 × S5 counterparts.

Comparison of the Linear Sigma Model and Chiral Perturbation Theory for Nucleon Properties

We compare the static nucleon properties in the Chiral Perturbation Theory (χPT) and the Linear Sigma Model (LSM). We consider a chiral model for the nucleon which is based on the linear sigma model with scalar-isoscalar and scalarisovector mesons coupled to quarks. We have solved the field equations in the mean field approximation for the hedgehog baryon state with different sets of model parameters. A good investigation of some static nucleon properties is obtained by the LSM.

Quantum dispersion relations for excitations of long folded spinning superstring in AdS 5 × S 5

We use AdS_5 x S^5 superstring sigma model perturbation theory to compute the leading one-loop corrections to the dispersion relations of the excitations near a long spinning string in AdS. This investigation is partially motivated by the OPE-based approach to the computation of the expectation value of null polygonal Wilson loops suggested in arXiv:1006.2788. Our results are in partial agreement with the recent asymptotic Bethe ansatz computation in arXiv:1010.5237. In particular, we find that the heaviest AdS mode (absent in the ABA approach) is stable and has a corrected one-loop dispersion relation similar to the other massive modes. Its stability might hold also at the next-to-leading order as we suggest using a unitarity-based argument.

On the non-renormalization of the AdS radius

We show that the relation between the 't Hooft coupling and the radius of AdS is not renormalized at one-loop in the sigma model perturbation theory. We prove this by computing the quantum effective action for the superstring on AdS5 × S5 and showing that it does not receive any finite α' corrections. We also show that the central charge of the interacting worldsheet conformal field theory vanishes at one-loop.

Comparison of the Extended Linear Sigma Model and Chiral Perturbation Theory for Nucleon Properties

We compare the extended linear sigma model and chiral perturbation theory in describing the static nucleon properties. A good description of some nucleon properties is obtained by the extended linear sigma model.

Scalar meson dynamics in chiral perturbation theory

A comparison of the linear sigma model (L$\sigma$M) and Chiral Perturbation Theory (ChPT) predictions for pion and kaon dynamics is presented. Lowest and next-to-leading order terms in the ChPT amplitudes are reproduced if one restricts to scalar resonance exchange. Some low energy constants of the order $p^4$ ChPT Lagrangian are fixed in terms of scalar meson masses. Present values of these low energy constants are compatible with the L$\sigma$M dynamics. We conclude that more accurate values would be most useful either to falsify the L$\sigma$M or to show its capability to shed some light on the controversial scalar physics.

Comments on D-brane interactions in PP-wave backgrounds

We calculate the interaction potential between widely separated D-branes in PP-wave backgrounds in string theory as well as in low-energy supergravity. Timelike and spacelike orientations are qualitatively different but in both cases the effective brane tensions and RR charges take the same values as in Minkowski space in accordance with the expectations from the sigma model perturbation theory.

Anomaly, fluxes and (2,0) heterotic-string compactifications

We compute the corrections to heterotic-string backgrounds with (2,0) world-sheet supersymmetry, up to two loops in sigma-model perturbation theory. We investigate the conditions for these backgrounds to preserve spacetime supersymmetry and we find that a sufficient requirement for consistency is the applicability of the $\partial\bar\partial$-lemma. In particular, we investigate the $\alpha'$ corrections to (2,0) heterotic-string compactifications and we find that the Calabi-Yau geometry of the internal space is deformed to a Hermitian one. We show that at first order in $\alpha'$, the heterotic anomaly-cancellation mechanism does not induce any lifting of moduli. We explicitly compute the corrections to the conifold and to the U(n)-invariant Calabi-Yau metric at first order in $\alpha'$. We also find a generalization of the gauge-field equations, compatible with the Donaldson equations on conformally-balanced Hermitian manifolds.

SEMICLASSICAL QUANTIZATION OF SUPERSTRINGS: AdS5 × S5 AND BEYOND

We discuss semiclassical quantization of closed superstrings in AdS 5 × S 5. We consider two basic examples: point-like string boosted along a large circle of S 5 and folded string rotating in AdS 5. In the first case we clarify the general structure of the sigma model perturbation theory for the energy of string states beyond the one-loop order (related to the plane-wave limit). In the second case we argue that the large spin limit of the expression for the ground-state energy (i.e. for the dimension of the corresponding minimal twist gauge theory operator) has the form S + f(λ) ln S to all orders in the [Formula: see text] expansion, in agreement with the AdS/CFT duality. We also suggest the extension of the semiclassical approach to near-conformal (near-AdS) cases on the example of the fractional D3-brane on conifold background.

One Loop Conformal Invariance of the Superstring in anAdS5×S5Background

It is proven that the pure spinor superstring in an AdS_5 x S^5 background remains conformally invariant at one loop level in the sigma model perturbation theory.

Two-loop test of Buscher’sTduality

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC

A FULL-ACCEPTANCE DETECTOR FOR SSC PHYSICS AT LOW AND INTERMEDIATE MASS SCALES: AN EXPRESSION OF INTEREST TO THE SSC

Rolling radii and a time-dependent dilation

Three families of solutions of the background field equations for the bosonic string are presented. These solutions describe a D-dimensional space-time for which the constant time slices are tori with D −1 “rolling radii” - that is, radii which are allowed to vary with time, along with a time-dependent dilation field. Each of the three families (which correspond to D = 26, D > 26, or D < 26) includes solutions where d radii increase as the other D− d−1 radii decrease, where 0⩽ d⩽ D − 1. It is shown that these solutions can be extended to order α' in nonlinear sigma model perturbation theory, and it is conjectured that this continues to any given order in α'.

The Born-Infeld action from conformal invariance of the open superstring

We show that the one-loop approximation to sigma-model perturbation theory for the open-superstring leads to the low-energy effective action of Born-Infeld for the gauge field coupled to the ends of the string. Thus the bosonic part of the low-energy open superstring effective action is just that of the open bosinic string. We also that these results are exact to all loop orders of sigma-model perturbation theory.

Nonperturbative effects on the string world sheet (II)

Nonperturbative effects in the sigma model describing string propagation in curved space are considered. While the space-time superpotential is not renormalized in sigma-model perturbation theory, we show that it is changed by nonperturbative effects. Instantons can generate tadpoles and thus destabilize certain vacuum configurations, they can give masses to particles which are massless in perturbation theory and they can modify Yukawa couplings and high dimension operators in the superpotential. We consider the effects of perturbation theory around the instanton and multi-instanton configurations. Certain effects (pairing of particles in 27 and in 27 and tadpoles in models with the spin connection equal to the gauge-connection) vanish in the instanton approximation. We argue that this is an exact result.