arXiv subjects

Barton Zwiebach

Publications and source records attributed to Barton Zwiebach.

At least 19 recordsLinked to original sources

arXiv2026

Universal quadratic field equations via homotopy algebras

We explain how the 'bar-cobar' construction for homotopy algebras reformulates the equations of motion of arbitrary gauge theories as gauge-covariant quadratic equations for an extended set of fields. The linear term of the new equations encodes the interactions of the original theory, while the quadratic term is universal. The extended fields include type-I multilocal fields, which depend on a set of coordinates and type-II multilocal fields, which depend on several sets of coordinates. The new equations of motion are the Maurer-Cartan equations of a differential graded associative algebra or Lie algebra. We show that every solution of the new equations is gauge equivalent to a solution with only type-I fields, that represents a solution of the original equations of motion. In string theory type-I fields are entangled states of the associated CFT, to be inserted across multiple punctures of a Riemann surface. General type-II states can also represent disconnected Riemann surfaces.

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arXiv2026

Gauge algebra and diffeomorphisms in string field theory

We consider the gauge algebra of closed string field theory with a focus on diffeomorphisms. This algebra contains off-shell information in two ways. The first way is geometric, through the choice of three-punctured sphere defining the three-string vertex. We establish that to leading order in derivatives the superstring algebra is universal: identical for any choice of vertex. For bosonic strings, however, some off-shell dependence remains for vertices that require symmetrization. Off-shell information also appears because field-dependent redefinition of the gauge parameters can alter the algebra. We analyze this dependence in the language of $L_\infty$ algebras, looking at the role of trivial gauge transformations in the efforts to demonstrate that standard diffeomorphisms are part of the string gauge symmetry.

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arXiv2025

Type II RR string fields and exotic diffeomorphisms

We study the theory of massless fields of type II strings arising from the string field theory that uses two string fields, a physical one and an extra one that allows the writing of an action, but whose degrees of freedom ultimately decouple. The mechanism allowing the description of the self-dual five-form of type IIB, anticipated by Sen, is used by the SFT to describe all Ramond-Ramond forms in type IIB and IIA in a manifestly duality-invariant way. We find explicit expressions for the leading terms in the gauge transformation of the RR fields and focus on diffeomorphisms, which are exotic for both the physical and the extra fields, perhaps as needed to describe propagating degrees of freedom that do not gravitate. The algebra of diffeomorphisms includes field-dependent structure constants and only closes on-shell, as predicted by the type II SFT gauge algebra.

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arXiv2024

String Field Theory: A Review

As of today there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings and type II strings. The construction of these theories require algebraic ingredients, such as $A_\infty$ and $L_\infty$ homotopy algebras, geometric ingredients, relevant to the building of moduli spaces of Riemann surfaces and the distribution of picture changing operators, and field-theoretic ingredients, involving two-dimensional CFT's and BCFT's and Batalin-Vilkovisky quantization. Applications of string field theory include the description of non-perturbative phenomena such as tachyon condensation and classical solutions, and the resolution of a number of ambiguities that bedevil the world-sheet formulation of perturbative string theory. It also allows, given a proper definition of contours of integration for momenta, for a proof of unitarity and a clear understanding of the ultraviolet finiteness of the theory. In this article we review these developments.

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arXiv2024

On the normalization of open-closed string amplitudes

We use the factorization constraints of open-closed string field theory to determine the signs and normalizations of general string amplitudes with both open and closed string external states. The normalization of all amplitudes is controlled by the genus, the number of boundaries, the number of open and closed string insertions, the string coupling and the D-brane tension. The challenge with signs arises because the relevant moduli spaces are not complex manifolds and have no obvious orientation. We deal with this by fixing a specific convention for the sign of the integration measure over the moduli space and adopting a consistent prescription for the ordering of operators and ghost insertions inside correlators.

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arXiv2023

On black hole singularity resolution in $D=2$ via duality-invariant $α'$ corrections

Starting with the two-derivative limit of $D=2$ string theory, we explore the space of T-duality invariant $α'$ corrections, a space that contains a point representing the fully $α'$-corrected classical string theory. Using a parametrization introduced by Gasperini and Veneziano we obtain black hole solutions in this theory space. We prove that the dual of a solution with a regular horizon must have a curvature singularity. We find regions in the theory space where the black hole is deformed while preserving the horizon and the singularity, and regions where no black hole appears to exist. Furthermore, we find subregions in this theory space, probably not containing string theory, in which the black hole geometry exhibits a horizon leading to an interior that, having no singularity in the metric, curvature, or dilaton, is a regular cosmology.

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arXiv2023

2D Black Holes, Bianchi I Cosmologies, and $α'$

We report two surprising results on $α'$ corrections in string theory restricted to massless fields. First, for critical dimension Bianchi type I cosmologies with $q$ scale factors only $q-1$ of them have non-trivial $α'$ corrections. In particular, for FRW backgrounds all $α'$ corrections are trivial. Second, in non-critical dimensions, all terms in the spacetime action other than the cosmological term are field redefinition equivalent to terms with arbitrarily many derivatives, with the latter generally of the same order. Assuming an $α'$ expansion with coefficients that fall off sufficiently fast, we consider field redefinitions consistent with this fall-off and classify the higher derivative terms for two-dimensional string theory with one timelike isometry. This most general duality-invariant theory permits black-hole solutions, and we provide perturbative and non-perturbative tools to explore them.

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arXiv2021

Initial value problem in string-inspired nonlocal field theory

We consider a nonlocal scalar field theory inspired by the tachyon action in open string field theory. The Lorentz-covariant action is characterized by a parameter $ξ^2$ that quantifies the amount of nonlocality. Restricting to purely time-dependent configurations, we show that a field redefinition perturbative in $ξ^2$ reduces the action to a local two-derivative theory with a $ξ^2$-dependent potential. This picture is supported by evidence that the redefinition maps the wildly oscillating rolling tachyon solutions of the nonlocal theory to conventional rolling in the new scalar potential. For general field configurations we exhibit an obstruction to a local Lorentz-covariant formulation, but we can still achieve a formulation local in time, as well as a light-cone formulation. These constructions provide an initial value formulation and a Hamiltonian. Their causality is consistent with a lack of superluminal behavior in the nonlocal theory.

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arXiv2019

Hyperbolic String Vertices

The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. We present a homological proof of existence of string vertices and their uniqueness up to canonical transformations. Using hyperbolic metrics on surfaces with geodesic boundaries we give an exact construction of string vertices as sets of surfaces with systole greater than or equal to $L$ with $L\leq 2\, \hbox{arcsinh}\, 1$. Intrinsic hyperbolic collars prevent the appearance of short geodesics upon sewing. The surfaces generated by Feynman diagrams are naturally endowed with Thurston metrics: hyperbolic on the vertices and flat on the propagators. For the classical theory the length $L$ is arbitrary and, as $L\to \infty$ hyperbolic vertices become the minimal-area vertices of closed string theory.

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arXiv2019

Extremal isosystolic metrics with multiple bands of crossing geodesics

We apply recently developed convex programs to find the minimal-area Riemannian metric on $2n$-sided polygons ($n\geq 3$) with length conditions on curves joining opposite sides. We argue that the Riemannian extremal metric coincides with the conformal extremal metric on the regular $2n$-gon. The hexagon was considered by Calabi. The region covered by the maximal number $n$ of geodesics bands extends over most of the surface and exhibits positive curvature. As $n\to \infty$ the metric, away from the boundary, approaches the well-known round extremal metric on $\mathbb{RP}_2$. We extend Calabi's isosystolic variational principle to the case of regions with more than three bands of systolic geodesics. The extremal metric on $\mathbb{RP}_2$ is a stationary point of this functional applied to a surface with infinite number of systolic bands.

math.DG↗

arXiv2019

Convex programs for minimal-area problems

The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. This is an extremal length problem in conformal geometry as well as a problem in systolic geometry. We consider the analogous minimal-area problem for homology classes of curves and, with the aid of calibrations and the max flow-min cut theorem, formulate it as a local convex program. We derive an equivalent dual program involving maximization of a concave functional. These two programs give new insights into the form of the minimal-area metric and are amenable to numerical solution. We explain how the homology problem can be modified to provide the solution to the original homotopy problem.

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arXiv2019

Minimal-area metrics on the Swiss cross and punctured torus

The closed string field theory minimal-area problem asks for the conformal metric of least area on a Riemann surface with the condition that all non-contractible closed curves have length at least 2π. Through every point in such a metric there is a geodesic that saturates the length condition, and saturating geodesics in a given homotopy class form a band. The extremal metric is unknown when bands of geodesics cross, as it happens for surfaces of non-zero genus. We use recently proposed convex programs to numerically find the minimal-area metric on the square torus with a square boundary, for various sizes of the boundary. For large enough boundary the problem is equivalent to the "Swiss cross" challenge posed by Strebel. We find that the metric is positively curved in the two-band region and flat in the single-band regions. For small boundary the metric develops a third band of geodesics wrapping around it, and has both regions of positive and negative curvature. This surface can be completed to provide the minimal-area metric on a once-punctured torus, representing a closed-string tadpole diagram.

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arXiv2019

Duality Invariant Cosmology to all Orders in $α'$

While the classification of $α'$ corrections of string inspired effective theories remains an unsolved problem, we show how to classify duality invariant $α'$ corrections for purely time-dependent (cosmological) backgrounds. We determine the most general duality invariant theory to all orders in $α'$ for the metric, $b$-field, and dilaton. The resulting Friedmann equations are studied when the spatial metric is a time-dependent scale factor times the Euclidean metric and the $b$-field vanishes. These equations can be integrated perturbatively to any order in $α'$. We construct non-perturbative solutions and display duality invariant theories featuring string-frame de Sitter vacua.

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arXiv2019

Non-perturbative de Sitter vacua via $α'$ corrections

The higher-derivative $α'$ corrections consistent with $O(d,d)$ duality invariance can be completely classified for cosmological, purely time-dependent backgrounds. This result is used to show that there are duality invariant theories featuring string-frame de Sitter vacua as solutions that are non-perturbative in $α'$, thus suggesting that classical string theory may realize de Sitter solutions in an unexpected fashion.

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arXiv2017

$L_{\infty}$ Algebras and Field Theory

We review and develop the general properties of $L_\infty$ algebras focusing on the gauge structure of the associated field theories. Motivated by the $L_\infty$ homotopy Lie algebra of closed string field theory and the work of Roytenberg and Weinstein describing the Courant bracket in this language we investigate the $L_\infty$ structure of general gauge invariant perturbative field theories. We sketch such formulations for non-abelian gauge theories, Einstein gravity, and for double field theory. We find that there is an $L_\infty$ algebra for the gauge structure and a larger one for the full interacting field theory. Theories where the gauge structure is a strict Lie algebra often require the full $L_\infty$ algebra for the interacting theory. The analysis suggests that $L_\infty$ algebras provide a classification of perturbative gauge invariant classical field theories.

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arXiv2016

On the curious spectrum of duality invariant higher-derivative gravity

We analyze the spectrum of the exactly duality and gauge invariant higher-derivative double field theory. While this theory is based on a chiral CFT and does not correspond to a standard string theory, our analysis illuminates a number of issues central in string theory. The full quadratic action is rewritten as a two-derivative theory with additional fields. This allows for a simple analysis of the spectrum, which contains two massive spin-2 ghosts and massive scalars, in addition to the massless fields. Moreover, in this formulation, the massless or tensionless limit $α'\rightarrow \infty$ is non-singular and leads to an enhanced gauge symmetry. We show that the massive modes can be integrated out exactly at the quadratic level, leading to an infinite series of higher-derivative corrections. Finally, we present a ghost-free massive extension of linearized double field theory, which employs a novel mass term for the dilaton and metric.

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arXiv2016

Three-point Functions in Duality-Invariant Higher-Derivative Gravity

Doubled $α'$-geometry is the simplest higher-derivative gravitational theory with exact global duality symmetry. We use the double metric formulation of this theory to compute on-shell three-point functions to all orders in $α'$. A simple pattern emerges when comparing with the analogous bosonic and heterotic three-point functions. As in these theories, the amplitudes factorize. The theory has no Gauss-Bonnet term, but contains a Riemann-cubed interaction to second order in $α'$.

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arXiv2015

T-duality Constraints on Higher Derivatives Revisited

We ask to what extent are the higher-derivative corrections of string theory constrained by T-duality. The seminal early work by Meissner tests T-duality by reduction to one dimension using a distinguished choice of field variables in which the bosonic string action takes a Gauss-Bonnet-type form. By analyzing all field redefinitions that may or may not be duality covariant and may or may not be gauge covariant we extend the procedure to test T-duality starting from an action expressed in arbitrary field variables. We illustrate the method by showing that it determines uniquely the first-order $α'$ corrections of the bosonic string, up to terms that vanish in one dimension. We also use the method to glean information about the ${\cal O}(α'^2)$ corrections in the double field theory with Green-Schwarz deformation.

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