String Effective Action Research Articles

Tree-level R4 correction from O(d, d): NS-NS five-point terms

The tree-level string effective action reduced from D to D − d dimensions possesses a continuous O(d, d) symmetry, closely related to T-duality. A necessary condition for a higher derivative correction to preserve this symmetry is that certain O(d, d) violating terms which appear in the dimensional reduction have to cancel out. We use this idea to complete the quartic Riemann correction with all terms involving five NS-NS sector fields. The resulting Lagrangian is considerably simpler than expressions that have previously appeared in the literature.

Worldsheet contributions to instantons in string effective field theories

The D-instantons in [Formula: see text] theory can contribute to the string effective action. The relation with the D-instanton term in Type IIB string theory will be clarified. The equation of the scalar field is projected to the two-dimensional worldsheet, on which a [Formula: see text] conformal field theory may be formulated. The energies of primary states in a minimal [Formula: see text] theory coupled to a [Formula: see text] topological string are evaluated and compared with the particle spectrum.

Revisiting α′ corrections to heterotic two-charge black holes

We find solutions of the heterotic string effective action describing the first-order α′ corrections to two-charge black holes at finite temperature. Making explicit use of these solutions, we compute the corrections to the thermodynamic quantities: temperature, chemical potentials, mass, charges and entropy. We check that the first law of black hole mechanics is satisfied and that the thermodynamics agrees with the one extracted from the Euclidean on-shell action. Finally, we show that our results are in agreement with the corrections for the thermodynamics recently predicted by Chen, Maldacena and Witten.

On AdS/CFT duality in the twisted sector of string theory on AdS5× S5/ℤ2 orbifold background

We consider type IIB string theory on an AdS5 × S5/ℤ2 orbifold background, which should be dual to 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal SU(N) × SU(N) gauge theory with two bi-fundamental hypermultiplets. The correlator of two chiral BPS operators from the twisted sector of this quiver CFT exhibits non-trivial dependence on the ’t Hooft coupling λ already in the planar limit. This dependence was recently determined using localisation and the expansion at large λ contains a subleading contribution proportional to ζ(3)λ−3/2. We address the question of how to reproduce this correction on the string theory side by starting with the ζ(3)α′3 term in the type IIB string effective action. We find a regular solution of type IIB supergravity which represents a resolution of the AdS5 × S5/ℤ2 orbifold and demonstrate that the relevant light twisted sector states may be identified as additional supergravity 2-form modes “wrapping” a finite 2-cycle in the resolution space. Reproducing the structure of the gauge theory result becomes more transparent in the large R-charge or BMN-like limit in which the resolved background takes a pp-wave form with the transverse space being a product of ℝ4 and the Eguchi-Hanson space.

Exploring the β symmetry of supergravity

Kaluza-Klein reductions of low energy string effective actions possess a continuous O(d, d) symmetry. The non-geometric elements of this group, parameterized by a bi-vector β, are not inherited from the symmetries of the higher-dimensional theory, but constitute instead a symmetry enhancement produced by the isometries of the background. The realization of this enhancement in the parent theory was recently defined as β symmetry, a powerful tool that allows to avoid the field reparameterizations of the Kaluza-Klein procedure. In this paper we further explore this symmetry and its impact on the first order α′-corrections. We derive the β transformation rules from the frame formulation of Double Field Theory (DFT), and connect them to the corresponding rules in the Metsaev-Tseytlin and Bergshoeff-de Roo supergravity schemes. It follows from our results that β symmetry is a necessary condition for the uplift of string α′-expansions to DFT.

Palatini variation in generalized geometry and string effective actions

We develop the Palatini formalism within the framework of generalized Riemannian geometry of Courant algebroids. In this context, the Palatini variation of a generalized Einstein–Hilbert–Palatini action - formed using a generalized metric, a Courant algebroid connection (in contrary to the ordinary case, not necessarily a torsionless one) and a volume form - leads naturally to a proper notion of a generalized Levi-Civita connection and low-energy effective actions of string theory.

Non-planar corrections in orbifold/orientifold mathcal{N} = 2 superconformal theories from localization

We study non-planar corrections in two special mathcal{N} = 2 superconformal SU(N) gauge theories that are planar-equivalent to mathcal{N} = 4 SYM theory: two-nodes quiver model with equal couplings and mathcal{N} = 2 vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. We focus on two observables in these theories that admit representation in terms of localization matrix model: free energy on 4-sphere and the expectation value of half-BPS circular Wilson loop. We extend the methods developed in arXiv:2207.11475 to derive a systematical expansion of non-planar corrections to these observables at strong ’t Hooft coupling constant λ. We show that the leading non- planar corrections are given by a power series in λ3/2/N2 with rational coefficients. Sending N and the coupling constant λ to infinity with λ3/2/N2 kept fixed corresponds to the familiar double scaling limit in matrix models. We find that in this limit the observables in the two models are related in a remarkably simple way: the free energies differ by the factor of 2, whereas the Wilson loop expectation values coincide. Surprisingly, these relations hold only at strong coupling, they are not valid in the weak coupling regime. We also discuss a dual string theory interpretation of the leading corrections to the free energy in the double scaling limit suggesting their relation to curvature corrections in type IIB string effective action.

The α′2 correction from double field theory

It is known that the order α′ correction to the tree-level effective action for the bosonic and heterotic string can be described in the framework of Double Field Theory (DFT). Here we determine the DFT action and transformations at order α′2 by a direct calculation. The result is vastly simpler than previous proposals. We show that this correction reproduces the known α′2 correction to the heterotic string effective action. The relation of our action to an (implicit) all order proposal coming from the so-called generalized Bergshoeff-de Roo identification is also discussed.

Completing R4 using O(d, d)

The tree-level string effective action is known to contain quartic Riemann terms with coefficient ζ(3)α′3. In the case of the type II string this is the first α′ correction. We use the requirement that the action reduced on a d-torus should have an O(d, d) symmetry to find the B-field couplings up to fifth order in fields. The answer turns out to have a surprisingly intricate structure.

Fine corrections in the effective string describing SU(2) Yang-Mills theory in three dimensions

We present a study of the effective string that describes the infrared dynamics of SU(2) Yang-Mills theory in three dimensions. By combining high-precision lattice simulation results for Polyakov-loop correlators at finite temperatures close to (and less than) the deconfinement one with the analytical constraints from renormalization-group arguments, from the exact integrability of the two-dimensional Ising model that describes the universality class of the critical point of the theory, from conformal perturbation theory, and from Lorentz invariance, we derive tight quantitative bounds on the corrections to the effective string action beyond the Nambu-Gotō approximation. We show that these corrections are compatible with the predictions derived from a bootstrap analysis of the effective string theory, and have a value which does not allow to prove the Axionic String Ansatz for this model.

Cosmic acceleration from string induced Galileons

It has been shown a specific Horndeski theory of gravity arises from a consistent Kaluza-Klein reduction of the gravi-dilaton sector of the low-energy effective heterotic string action with a first α' correction. Here we provide a first investigation of the cosmological solutions to the lower dimensional theory by constructing exact solutions to the field equations in various frames. At tree level, in string frame, we find the duality symmetry of the parent theory is unaltered by dimensional reduction, leading to standard bouncing and pre-Big Bang scenario solutions. For α'≠0, we uncover exact models exhibiting cosmic acceleration, where we find interesting physics concerning the number of noncompact dimensions. Certain stability requirements demand the inclusion of a dilaton potential.

Supersymmetry, T-duality and heterotic \u03b1\u2032-corrections

Higher-derivative interactions and transformation rules of the fields in the effective field theories of the massless string states are strongly constrained by space-time symmetries and dualities. Here we use an exact formulation of ten dimensional mathcal{N} = 1 supergravity coupled to Yang-Mills with manifest T-duality symmetry to construct the first order α′-corrections of the heterotic string effective action. The theory contains a supersymmetric and T-duality covariant generalization of the Green-Schwarz mechanism that determines the modifications to the leading order supersymmetry transformation rules of the fields. We compute the resulting field-dependent deformations of the coefficients in the supersymmetry algebra and construct the invariant action, with up to and including four-derivative terms of all the massless bosonic and fermionic fields of the heterotic string spectrum.

Cutkosky rules and unitarity (violation) in D-instanton amplitudes

In perturbative amplitudes in quantum field theory and string field theory, Cutkosky rule expresses the anti-hermitian part of a Feynman diagram in terms of sum over all its cut diagrams, and this in turn is used to prove unitarity of the theory. For D-instanton contribution to a string theory amplitude, the cutting rule needed for the proof of unitarity is somewhat different; we need to sum over only those cut diagrams for which all the world-sheet boundaries ending on some particular D-instanton lie on the same side of the cut. By working with the closed string effective action, obtained after integrating out the open string modes, we prove that the D-instanton amplitudes actually satisfy these cutting rules, provided the effective action is real. The violation of unitarity in the closed string sector of two dimensional string theory can be traced to the failure of this reality condition. In the critical superstring theory, multi-instanton and multi anti-instanton amplitudes satisfy the reality condition. Contribution to the amplitudes from the instanton anti-instanton sector satisfies the reality condition if we make a specific choice of integration cycle over the configuration space of string fields, whereas contribution due to the non-BPS D-instantons will need to either vanish or have an overall real normalization in order for it to give real contribution. We use Picard-Lefschetz theory to argue that these conditions are indeed satisfied in superstring theories.

Derive Lovelock gravity from string theory in cosmological background

It was proved more than three decades ago, that the first order α′ correction of string effective theory could be written as the Gauss-Bonnet term, which is the quadratic term of Lovelock gravity. In cosmological background, with an appropriate field redefinition, we reorganize the infinite α′ corrections of string effective action into a finite term expression for any specific dimension. This finite term expression matches Lovelock gravity exactly and thus fix the couplings of Lovelock gravity by the coefficients of string effective action. This result thus provides a strong support to string theory.

Private life of the Liouville field that causes new anomalies in the Nambu-Goto string

I consider higher-order terms of the Seeley expansion of the heat kernel, which for smooth metrics are suppressed as inverse powers of the UV cutoff Λ, and demonstrate how they result in an anomalous contribution to the string effective action after doing uncertainties Λ−2×Λ2. For the Polyakov string these anomalies precisely reproduce at one loop the result of KPZ-DDK obtained for the Liouville theory by the conformal field theory technique. For the Nambu-Goto string I find a deviation from this result which shows that the two string formulations may differ.

Quantum String Cosmology

We present a short review of possible applications of the Wheeler-De Witt equation to cosmological models based on the low-energy string effective action, and characterised by an initial regime of asymptotically flat, low energy, weak coupling evolution. Considering in particular a class of duality-related (but classically disconnected) background solutions, we shall discuss the possibility of quantum transitions between the phases of pre-big bang and post-big bang evolution. We will show that it is possible, in such a context, to represent the birth of our Universe as a quantum process of tunneling or “anti-tunneling” from an initial state asymptotically approaching the string perturbative vacuum.

Classical and quantum (2+1)-dimensional spatially homogeneous string cosmology

We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous (2+1)-dimensional space-times with the sources given by the contributions of dilaton, antisymmetric gauge B-field, and central charge deficit term varLambda . At the quantum level, solutions of Wheeler–DeWitt equations have been enriched by considering the quantum versions of the classical conditional symmetry equations. Concerning the possible applications of the obtained solutions, the semiclassical analysis of Bohm’s mechanics has been performed to demonstrate the possibility of avoiding the classical singularities at the quantum level.

T-dualization of G\xf6del string cosmologies via Poisson\u2013Lie T-duality approach

Using the homogeneous Gödel spacetimes we find some new solutions for the field equations of bosonic string effective action up to first order in alpha ' including both dilaton and axion fields. We then discuss in detail the (non-)Abelian T-dualization of Gödel string cosmologies via the Poisson–Lie (PL) T-duality approach. In studying Abelian T-duality of the models we get seven dual models in such a way that they are constructed by one-, two- and three-dimensional Abelian Lie groups acting freely on the target space manifold. The results of our study show that the Abelian T-dual models are, under some of the special conditions, self-dual; moreover, by applying the usual rules of Abelian T-duality without further corrections, we are still able to obtain two-loop solutions. We also study the Abelian T-duality of Gödel string cosmologies up to alpha '-corrections by using the T-duality rules at two-loop order derived by Kaloper and Meissner. Afterwards, non-Abelian duals of the Gödel spacetimes are constructed by two- and three-dimensional non-Abelian Lie groups such as A_2, A_2 oplus A_1 and SL(2, mathbb {R}). In this way, the PL self-duality of AdS_3 times mathbb {R} space is discussed.

On the quantization of folded strings in non-critical dimensions

Classical rotating closed string are folded strings. At the folding points the scalar curvature associated with the induced metric diverges. As a consequence one cannot properly quantize the fluctuations around the classical solution since there is no complete set of normalizable eigenmodes. Furthermore in the non-critical effective string action of Polchinski and Strominger, there is a divergence associated with the folds. We overcome this obstacle by putting a massive particle at each folding point which can be used as a regulator. Using this method we compute the spectrum of quantum fluctuations around the rotating string and the intercept of the leading Regge trajectory. The results we find are that the intercepts are a = 1 and a = 2 for the open and closed string respectively, independent of the target space dimension. We argue that in generic theories with an effective string description, one can expect corrections from finite masses associated with either the endpoints of an open string or the folding points on a closed string. We compute explicitly the corrections in the presence of these masses.

Finite-size effects in the rough phase of the 3d Ising model

Using Monte Carlo simulations, finite-size effects of interfacial properties in the rough phase of the Ising on a cubic lattice with L×L×R sites are studied. In particular, magnetization profiles perpendicular to the flat interface of size L×R are studied, with L being considerably larger than R, in the (pre)critical temperature range. The resulting R-dependences are compared with predictions of the standard capillary-wave theory, in the Gaussian approximation, and with a field theory based on effective string actions, for L=∞.