Effective Action Of String Theory Research Articles

Large D gravity and low D string via α′ corrections

In this paper, we generalize the correspondence between large D gravity and low D string theory to the most general case, including its T-dual solutions. It is well-known that the large D limit of the Schwarzschild-Tangherlini black hole in gravity becomes a two-dimensional near-horizon geometry. Similarly, the large D limit of its T-dual solution, obtained by the Buscher rules, namely the string black hole with a naked singularity, reduces to a two-dimensional near-singularity geometry. Both of these geometries are described by the two-dimensional low-energy effective action of string theory and are related to each other by scale-factor duality. Secondly, we demonstrate that these near-horizon/singuglarity geometries, including complete α′ corrections, can be described by the two-dimensional Hohm-Zwiebach action. This approach allows for the derivation of non-perturbative and non-singular solutions. Furthermore, the Hohm-Zwiebach action provides a systematic way to investigate the α′-corrected near-horizon/singularity geometries of different kinds of black holes, which are difficult to achieve through the Wess-Zumino-Witten (WZW) model method.

A positive metric over DGKT vacua

We study the notion of a metric over the space of AdS solution in string theory, leading to an associated distance between them. Such a distance is the idea underlying the AdS distance conjecture. We utilise the previously developed prescription for extracting such a metric: taking an off-shell quadratic variation of the string theory effective action and then evaluating it over the space of on-shell solutions. It was shown that this prescription leads to a well-defined positive metric over M-theory Freund-Rubin vacua. In this work, we use the same prescription to calculate the metric over type IIA DGKT vacua. These are much more involved, they have multiple flux parameters and exhibit scale separation. While it remains an open question whether these vacua exist as fully localised solutions of string theory, they are well-defined within the four-dimensional effective theory, which is all that is required for the calculation. We find that they also have a positive metric over them. Interestingly, this metric turns out to be independent of the many flux parameters in the solution, similarly to what happens for metrics over scalar field spaces. This non-trivial flux cancellation, as well as results from explicit vacua, lead us to propose a Swampland condition: that the metric over the space of vacua in quantum gravity, as defined by the above prescription, is always positive.

More on β-symmetry

Recent work has proposed a method for imposing T-duality on the metric, B-field, and dilaton of the classical effective action of string theory without using Kaluza-Klein reduction. Specifically, the D-dimensional effective action should be invariant under global O(D,D) transformations, provided that the partial derivatives along the β-parameters of the non-geometrical elements of the O(D,D) group become zero. In this paper, we speculate that the global β-symmetry can be utilized to identify both bulk and boundary couplings.We demonstrate that the Gibbons-Hawking term at the leading order of α′ is reproduced by this symmetry. Additionally, for closed spacetime manifolds at order α′, we show that the 20 independent geometrical couplings at this order are fixed by this symmetry up to field redefinitions. Specifically, we show that the invariance of the most general covariant and gauge invariant bulk action at order α′ under the most general covariant deformed β-transformation at order α′ fixes the action up to 13 parameters. These parameters reflect the field redefinitions freedom for the closed spacetime manifolds. For particular values of these parameters, we recover the effective action in the Metsaev-Tseytlin and in the Meissner schemes.

Upper bound on the Atiyah-Singer index from tadpole cancellation

We propose an upper bound on the Atiyah-Singer index in the effective action of string theory. For E8×E8′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {E}_8^{\\prime } $$\\end{document} and SO(32) heterotic string theories on smooth Calabi-Yau threefolds with line bundles, we find that the tadpole cancellation and supersymmetry conditions lead to an upper bound on the generation number of quarks and leptons as well as Higgs doublets. By taking into account the observed value of four-dimensional gauge couplings and the supergravity approximation, we explicitly evaluate the bound on favorable complete intersection Calabi-Yau threefolds. The bound can be extended to Calabi-Yau threefolds in the Kreuzer-Skarke database. We also put the upper bound on the Atiyah-Singer index in Type IIB/F-theory compactifications.

T-duality constraint on effective Lagrangians

Recent studies have highlighted the significant role of utilizing O(1, 1) symmetry in the circular reduction of effective actions to determine NS–NS couplings in the effective action of string theory. However, these calculations often result in residual terms as total derivatives that do not conform to O(1, 1) transformations. In this paper, we present explicit calculations at α′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha '$$\\end{document} order, demonstrating the enforceability of this symmetry on effective Lagrangians to establish the parameters governing covariant couplings in any scheme. Notably, we discover the O(1, 1)-invariant Lagrangians corresponding to the Metsaev–Tseytlin action and the Meissner action.

Slowly rotating and accelerating α′ -corrected black holes in four and higher dimensions

We consider the low-energy effective action of string theory at order $\alpha '$, including $R^2$-corrections to the Einstein-Hilbert gravitational action and non-trivial dilaton coupling. By means of a convenient field redefinition, we manage to express the theory in a frame that enables us to solve its field equations analytically and perturbatively in $\alpha ' $ for a static spherically symmetric ansatz in an arbitrary number of dimensions. The set of solutions we obtain is compatible with asymptotically flat geometries exhibiting a regular event horizon at which the dilaton is well-behaved. For the 4-dimensional case, we also derive the stationary black hole configuration at first order in $\alpha '$ and in the slowly rotating approximation. This yields string theory modifications to the Kerr geometry, including terms of the form $a$, $a^2$, $\alpha '$ and $a\alpha '$. In addition, we obtain the first $\alpha'$ correction to the C-metrics, which accommodates accelerating black holes. We work in the string frame and discuss the connection to the Einstein frame, for which rotating black holes have already been obtained in the literature.

Stability of the nonperturbative O(D,D) de Sitter spacetime: The isotropic case

The existence of de-Sitter solutions and their stability within string theory became, in recent years, one of the central research questions within the string theory community. The so-called de-Sitter conjecture states that the de-Sitter vacua are unstable within string theory. Here, we study the de-Sitter solutions in string theory and their stability in the time direction using the $O(d,d)$ symmetry approach allowing for the calculation of the generic form of the string theory effective action. We study the undiscussed case of the constant generalized dilaton as well as the general form of dilaton couplings. Our findings suggest that de-Sitter solutions are unstable for the constant generalized dilaton both with and without matter. Furthermore, we found that in order for the theory to be weakly coupled the general form of dilaton coupling is in the form of a cosmological constant.

Compact stars admitting Finch-Skea symmetry in the presence of various matter fields* *PKS acknowledges National Board for Higher Mathematics (NBHM) under Department of Atomic Energy (DAE), Govt. of India for financial support to carry out the Research project No.: 02011/3/2022 NBHM (R.P.)/R#D II/2152 Dt.14.02.2022. Sokoliuk O. performed the work in frame of the "Mathematical modeling in interdisciplinary research of processes

In the present study, we investigate the anisotropic stellar solutions admitting Finch-Skea symmetry (viable and non-singular metric potentials) in the presence of some exotic matter fields, such as Bose-Einstein Condensate (BEC) dark matter, the Kalb-Ramond fully anisotropic rank-2 tensor field from the low-energy string theory effective action, and the gauge field imposing symmetry. Interior spacetime is matched with both Schwarzchild and Reissner-Nördstrom vacuum spacetimes for BEC, KB, and gauge fields. In addition, we study the energy conditions, Equation of State (EoS), radial derivatives of energy density and anisotropic pressures, Tolman-Oppenheimer-Volkoff equilibrium condition, relativistic adiabatic index, sound speed, and surface redshift. Most of the aforementioned conditions are satisfied. Therefore, the solutions derived in the current study lie in the physically acceptable regime.

Tameness, Strings, and the Distance Conjecture

The Distance Conjecture states that an infinite tower of modes becomes exponentially light when approaching an infinite distance point in field space. We argue that the inherent path-dependence of this statement can be addressed when combining the Distance Conjecture with the recent Tameness Conjecture. The latter asserts that effective theories are described by tame geometry and implements strong finiteness constraints on coupling functions and field spaces. By exploiting these tameness constraints we argue that the region near the infinite distance point admits a decomposition into finitely many sectors in which path-independent statements for the associated towers of states can be established. We then introduce a more constrained class of tame functions with at most polynomial asymptotic growth and argue that they suffice to describe the known string theory effective actions. Remarkably, the multi-field dependence of such functions can be reconstructed by one-dimensional linear test paths in each sector near the boundary. In four-dimensional effective theories, these test paths are traced out as a discrete set of cosmic string solutions. This indicates that such cosmic string solutions can serve as powerful tool to study the near-boundary field space region of any four-dimensional effective field theory. To illustrate these general observations we discuss the central role of tameness and cosmic string solutions in Calabi-Yau compactifications of Type IIB string theory.

Higher-derivative field redefinitions in the presence of boundary

Recently it has been proposed that the consistency with T-duality requires the effective action of string theory at order alpha '^n to satisfy the least action principle provided that the values of the massless fields and their derivatives up to order n are known on the boundary. In this paper we speculate that this boundary condition constrains the field redefinitions and the corrections to the T-duality transformations in the presence of boundary, e.g., at order alpha ', the metric does not change, and all other massless fields should change to include only the first derivative of the massless fields. Using the above restricted field redefinitions, we write all gauge invariant bulk and boundary couplings in the bosonic string theory at order alpha ' in a minimal scheme. Then using the assumption that the effective action of string theory at the critical dimension is background independent, we fix the coefficients of the tree-level gauge invariant couplings by imposing O(1, 1) symmetry when the background has a circle and by imposing O(d, d) symmetry when the background has T^d. These constraints fix the bulk action up to an overall factor, and the boundary action up to two parameters. By requiring the gravity couplings in the boundary action to be consistent with those in the Chern-Simons gravity, the two boundary parameters are also fixed. Up to a restricted field redefinition, the bulk and boundary couplings are exactly those in the K.A. Meissner action and its corresponding boundary action.

Background independence of effective actions at critical dimension

Recently, by explicit calculations at orders $\alpha',\alpha'^2,\alpha'^3$, it has been observed that the effective action of string theory at the critical dimension is independent of the background for the closed spacetime manifolds. In this paper we speculate that for the open spacetime manifolds, the effective action is even independent of the character of the boundary, \ie the boundary couplings for timelike and spacelike boundaries are the same. We support this proposal by calculating the boundary couplings in the bosonic string theory at order $\alpha'$ for the spacelike boundary and show that they are the same as the couplings for the timelike boundary that have been recently found.

Effective action of string theory at order alpha ' in the presence of boundary

Recently, using the assumption that the string theory effective action at the critical dimension is background independent, the classical on-shell effective action of the bosonic string theory at order alpha ' in a spacetime manifold without boundary has been reproduced, up to an overall parameter, by imposing the O(1, 1) symmetry when the background has a circle. In the presence of the boundary, we consider a background which has boundary and a circle such that the unit normal vector of the boundary is independent of the circle. Then the O(1, 1) symmetry can fix the bulk action without using the lowest order equation of motion. Moreover, the above constraints and the constraint from the principle of the least action in the presence of boundary can fix the boundary action, up to five boundary parameters. In the least action principle, we assume that not only the values of the massless fields but also the values of their first derivatives are arbitrary on the boundary. We have also observed that the cosmological reduction of the leading order action in the presence of the Hawking–Gibbons boundary term, produces zero cosmological boundary action. Imposing this as another constraint on the boundary couplings at order alpha ', we find the boundary action up to two parameters. For a specific value for these two parameters, the gravity couplings in the boundary become the Chern–Simons gravity plus another term which has the Laplacian of the extrinsic curvature.

O(9,9) symmetry of NS-NS couplings at order α′3

Recently, imposing the $O(1,1)$ symmetry on the circle reduction of the classical effective action of string theory, we have found all NS-NS couplings of type II superstring theories at order $\alpha'^3$. In this paper we use the cosmological reduction on the couplings and show that, up to field redefinitions and total derivative terms, they are invariant under the $O(9,9)$ transformations.

O(25,\xa025) symmetry of bosonic string theory at order alpha '^2

It has been recently observed that the imposition of the O(1, 1) symmetry on the circle reduction of the classical effective action of string theory, can fix the effective action of the bosonic string theory at order alpha '^2, up to an overall factor. In this paper, we use the cosmological reduction on the action and show that, up to one-dimensional field redefinitions and total derivative terms, it can be written in the O(25, 25)-invariant form proposed by Hohm and Zwiebach.

Surface terms in effective action of O-plane at order alpha '^2

The effective action of string theory has both bulk and boundary terms if the spacetime is an open manifold. Recently, the known classical effective action of string theory at the leading order of alpha ' and its corresponding boundary action have been reproduced by constraining the effective actions to be invariant under gauge transformations and under string duality transformations. In this paper, we use this idea to find the classical effective action of the O-plane and its corresponding boundary terms in type II superstring theories at order alpha '^2 and for NS–NS couplings. We find that these constraints fix the bulk action and its corresponding boundary terms up to one overall factor. They also produce three multiplets in the boundary action that their coefficients are independent of the bulk couplings under the string dualities.

String-Inspired Running Vacuum—The “Vacuumon”—And the Swampland Criteria

We elaborate further on the compatibility of the “vacuumon potential” that characterises the inflationary phase of the running vacuum model (RVM) with the swampland criteria. The work is motivated by the fact that, as demonstrated recently by the authors, the RVM framework can be derived as an effective gravitational field theory stemming from underlying microscopic (critical) string theory models with gravitational anomalies, involving condensation of primordial gravitational waves. Although believed to be a classical scalar field description, not representing a fully fledged quantum field, we show here that the vacuumon potential satisfies certain swampland criteria for the relevant regime of parameters and field range. We link the criteria to the Gibbons–Hawking entropy that has been argued to characterise the RVM during the de Sitter phase. These results imply that the vacuumon may, after all, admit under certain conditions, a rôle as a quantum field during the inflationary (almost de Sitter) phase of the running vacuum. The conventional slow-roll interpretation of this field, however, fails just because it satisfies the swampland criteria. The RVM effective theory derived from the low-energy effective action of string theory does, however, successfully describe inflation thanks to the ∼H4 terms induced by the gravitational anomalous condensates. In addition, the stringy version of the RVM involves the Kalb–Ramond (KR) axion field, which, in contrast to the vacuumon, does perfectly satisfy the slow-roll condition. We conclude that the vacuumon description is not fully equivalent to the stringy formulation of the RVM. Our study provides a particularly interesting example of a successful phenomenological theory beyond the ΛCDM, such as the RVM, in which the fulfilment of the swampland criteria by the associated scalar field potential, along with its compatibility with (an appropriate form of) the weak gravity conjecture, prove to be insufficient conditions for warranting consistency of the scalar vacuum field representation as a faithful ultraviolet complete representation of the RVM at the quantum gravity level.

Classical algebraic structures in string theory effective actions

We study generic properties of string theory effective actions obtained by classically integrating out massive excitations from string field theories based on cyclic homotopy algebras of A∞ or L∞ type. We construct observables in the UV theory and we discuss their fate after integration-out. Furthermore, we discuss how to compose two subsequent integrations of degrees of freedom (horizontal composition) and how to integrate out degrees of freedom after deforming the UV theory with a new consistent interaction (vertical decomposition). We then apply our general results to the open bosonic string using Witten’s open string field theory. There we show how the horizontal composition can be used to systematically integrate out the Nakanishi-Lautrup field from the set of massless excitations, ending with a non-abelian A∞-gauge theory for just the open string gluon. Moreover we show how the vertical decomposition can be used to construct effective open-closed couplings by deforming Witten OSFT with a tadpole given by the Ellwood invariant. Also, we discuss how the effective theory controls the possibility of removing the tadpole in the microscopic theory, giving a new framework for studying D-brane deformations induced by changes in the closed string background.

T duality constraint on R-R couplings

It has been speculated that the metric, $B$-field and dilaton couplings in the low energy effective action of string theory at any order of $\alpha'$ may be found by imposing the gauge symmetries and the T-duality on the effective action. This proposal can be extended to include the Ramond-Ramond (R-R) couplings as well. In this paper, we first find the dimensional reduction of the R-R fields and then perform explicitly the T-duality constraint on the R-R couplings at the supergravity level. Up to an overall factor, it reproduces the democratic form of the R-R couplings.

Surface terms in the effective actions via duality constraints

The effective action of string theory on a spacetime manifold with boundary has both bulk and boundary terms. We propose that both bulk and boundary actions, may be found by imposing the effective action to be invariant under the gauge transformations and under the string dualities. Using this proposal at the leading order of α′, the standard Gibbons-Hawking-York boundary term is reproduced.

All higher-curvature gravities as Generalized quasi-topological gravities

Generalized quasi-topological gravities (GQTGs) are higher-curvature extensions of Einstein gravity characterized by the existence of non-hairy generalizations of the Schwarzschild black hole which satisfy gttgrr = –1, as well as for having second-order linearized equations around maximally symmetric backgrounds. In this paper we provide strong evidence that any gravitational effective action involving higher-curvature corrections is equivalent, via metric redefinitions, to some GQTG. In the case of theories involving invariants constructed from contractions of the Riemann tensor and the metric, we show this claim to be true as long as (at least) one non-trivial GQTG invariant exists at each order in curvature-and extremely conclusive evidence suggests this is the case in general dimensions. When covariant derivatives of the Riemann tensor are included, the evidence provided is not as definitive, but we still prove the claim explicitly for all theories including up to eight derivatives of the metric as well as for terms involving arbitrary contractions of two covariant derivatives of the Riemann tensor and any number of Riemann tensors. Our results suggest that the physics of generic higher-curvature gravity black holes is captured by their GQTG counterparts, dramatically easier to characterize and universal. As an example, we map the gravity sector of the Type-IIB string theory effective action in AdS5 at order \U0001d4aa (α′3) to a GQTG and show that the thermodynamic properties of black holes in both frames match.