arXiv subjects

Carlo Maccaferri

Publications and source records attributed to Carlo Maccaferri.

At least 19 recordsLinked to original sources

arXiv2026

Boundary observables in string field theory

Starting from the gauge invariant action for free string field theory with boundary recently constructed in 2506.05969, we define new gauge invariant observables which are analogous to the Brown-York charges of General Relativity. Just like the Brown-York charges, our observables originate from a boundary tadpole, and are associated to isometries of the SFT gauge group around a given background. The consistency of the construction requires the equation of motion of the background to be satisfied only at the boundary and therefore these observables can also be defined for backgrounds generated by sources in the bulk. As examples of our construction in open string field theory, we compute the flux through the boundary of constant electromagnetic field-strength solutions and the charge associated to the Coulomb solution. As a further example in closed string field theory, we characterize the infinite conserved charges associated to stringy-haired black-hole solutions in two-dimensional string theory. We also construct a generalization of these boundary observables to the full interacting string field theory.

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arXiv2025

Gauge-invariant action for free string field theory with boundary

We construct fully gauge-invariant kinetic terms for open and closed string field theories on a target space with boundary. This is realized by promoting the gauge parameters at the boundary to extra dynamical modes describing boundary degrees of freedom. Having a gauge-invariant classical action, we also construct the corresponding BV master action and show that the master equation is obeyed thanks to a peculiar nilpotent structure of the BV kinetic operator. From this general construction we explicitly derive free actions for massless and massive modes of open and closed strings propagating on a target with a boundary, including linear-dilaton backgrounds.

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arXiv2025

Boundary Modes in String Field Theory

We discuss the construction of boundary contributions to free string field theory actions in the context of the bosonic string. We show that it is generally possible to obtain a well-defined variational principle by adding a simple boundary term (which only depends on the value of the bulk fields at the boundary) to the original bulk action. However, it is in general not possible to do this in a gauge-invariant way unless suitable boundary degrees of freedom are added. We explicitly construct such boundary contributions for the massless level of both the open and the closed SFT, as well as for the tensionless limit of the full string field theory. Our results reproduce linearized general relativity with the Gibbons-Hawking-York term and provide similar gauge-invariant actions for the infinite tower of massless higher-spin gauge theories for all Regge trajectories. By writing down a gauge-invariant action for the first massive level of the open string, we provide evidence that an analogous construction should be possible for the full tensile string field theory.

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arXiv2024

Bulk-induced D-brane deformations and the string coupling constant

We consider computing the on-shell disk action of open-closed string field theory as a gauge-invariant way of capturing the shift in D-brane tension that is induced by a deformation of the bulk CFT. We study the effect of bulk matter deformations (both marginal and relevant) on a wide range of boundary conditions in a number of CFTs up to subleading (two-loop) order in perturbation theory. In all analyzed examples, we find that the shift in the $g$-function of the matter boundary state is always accompanied by a boundary-independent shift in the string coupling constant, whose leading behaviour is universally proportional to the sphere two-point function of the deforming bulk operator.

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arXiv2024

Adding stubs to quantum string field theories

Generalizing recent work by Schnabl-Stettinger and Erbin-Firat, we outline a universal algebraic procedure for `adding stubs' to string field theories obeying the BV quantum master equation. We apply our results to classical and quantum closed string field theory as well as to open-closed string field theory. We also clarify several aspects of the integration-out process in the co-algebraic formulation of string field theory at the quantum level.

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arXiv2024

String Field Theory

String Field Theory is a formulation of String Theory as a Quantum Field Theory in target space. It allows to tame the infrared divergences of String Theory and to approach its non-perturbative structure and background independence. This article gives a concise overview on the subject and of some of the main recent progress. Note: Review article for Oxford Research Encyclopedia of Physics

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arXiv2024

Introduction to String Theory

These are the lecture notes of the introductory String Theory course held by one of the authors for the master program of Theoretical Physics at Turin University. The world-sheet approach to String Theory is pedagogically introduced in the framework of the bosonic string and of the superstring.

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arXiv2023

Open-Closed String Field Theory in the Large $N$ Limit

We use the new nilpotent formulation of open-closed string field theory to explore the limit where the number $N$ of identical D-branes of the starting background is large. By reformulating the theory in terms of the 't Hooft coupling $λ=κN$, where $κ$ is the string coupling constant, we explicitly see that at large $N$ only genus zero vertices with arbitrary number of boundaries survive. After discussing the homotopy structure of the obtained large $N$ open-closed theory we discuss the possibility of integrating out the open string sector with a quantum but planar homotopy transfer. As a result we end up with a classical closed string field theory described by a weak $L_\infty$-algebra, containing a tree-level tadpole which, to first order in $λ$, is given by the initial boundary state. We discuss the possibility of removing the tadpole with a closed string vacuum shift solution, to end up with a new classical closed string background, where the initial D-branes have been turned into pure closed-string backreaction.

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arXiv2023

The Nilpotent Structure of Open-Closed String Field Theory

In this note we revisit the homotopy-algebraic structure of oriented bosonic open-closed string field theory and we give a new compact formulation in terms of a single cyclic open-closed coderivation which defines a single nilpotent structure describing the consistency of generic open-closed color-ordered off-shell amplitudes with arbitrary number of boundaries and at arbitrary genus.

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arXiv2022

The classical cosmological constant of open-closed string field theory

We consider deformations of D-brane systems induced by a change in the closed string background in the framework of bosonic open-closed string field theory, where it is possible to unambiguously tame infrared divergences originating from both open and closed string degenerations. A closed string classical solution induces a tadpole for the open strings which shifts the open string vacuum and generates a cosmological constant composed of two terms: one which is directly related to the closed string solution and the other which depends on the open string vacuum shift. We show that only the sum of these two terms is invariant under closed SFT gauge transformations and therefore is an observable. We conjecture that this observable is universally proportional to the shift in the world-sheet disk partition function between the starting D-brane in undeformed background and the final D-brane in deformed background, which typically includes also a change in the string coupling constant. We test the conjecture by considering a perturbative closed string solution describing deformations of a Narain compactification and, from the SFT cosmological constant, we reproduce the expected shift in the $g$-function of various D-branes living in the compactification. In doing this we are also able to identify a surprising change in the string coupling constant at second order in the deformation.

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arXiv2021

Closed string deformations in open string field theory I: bosonic string

This is the first of a series of three papers on open string field theories based on Witten star product deformed with a gauge invariant open/closed coupling. This deformation is a tree-level tadpole which destabilizes the initial perturbative vacuum. We discuss the existence of vacuum-shift solutions which cancel the tadpole and represent a new configuration where the initial D-brane system has adapted to the change in the closed string background. As an example we consider the bulk deformation which changes the compactification radius and, to first order in the deformation, we reproduce the shift in the mass of the open string KK modes from the new kinetic operator after the vacuum shift. We also discuss the possibility of taming closed string degenerations with the open string propagator in the simplest amplitude corresponding to two closed strings off a disk.

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arXiv2021

Closed string deformations in open string field theory II: superstring

This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed effective couplings in closed form. With the aim of getting all order results, we also construct a new observable in the $A_\infty$ theory in the small Hilbert space which correctly provides a gauge invariant coupling to physical closed strings and which descends from the WZW open-closed coupling upon partial gauge fixing and field redefinition. Armed with this new $A_\infty$ observable we use tensor co-algebra techniques to efficiently package the whole perturbation theory necessary for computing the effective action and we give all order results for the open-closed effective couplings in the small Hilbert space.

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arXiv2021

Closed string deformations in open string field theory III: ${\cal N}=2$ worldsheet localization

In this paper, which is the last of a series of three, we first verify that the two open-closed effective potentials derived in the previous paper from the WZW theory in the large Hilbert space and the $A_\infty$ theory in the small Hilbert space have the same vacuum structure. In particular, we show that mass-term deformations given by the effective (two open)-(one closed) couplings are the same, provided the effective tadpole is vanishing to first order in the closed string deformation. We show that this condition is always realized when the worldsheet BCFT enjoys a global ${\cal N}=2$ superconformal symmetry and the deforming closed string belongs to the chiral ring in both the holomorphic and anti-holomorphic sector. In this case it is possible to explicitly evaluate the mass deformation by localizing the SFT Feynman diagrams to the boundary of world-sheet moduli space, reducing the amplitude to a simple open string two-point function. As a non-trivial check of our construction we couple a constant Kalb-Ramond closed string state to the OSFT on the $\text{D}3$--$\text{D}(-1)$ system and we show that half of the bosonic blowing-up moduli become tachyonic, making the system condense to a bound state whose binding energy we compute exactly to second order in the closed string deformation, finding agreement with the literature.

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arXiv2020

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 $A_\infty$ or $L_\infty$ 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 $A_\infty$-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-branes deformations induced by changes in the closed string background.

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arXiv2020

Localization of effective actions in Heterotic String Field Theory

We consider the algebraic couplings in the tree level effective action of the heterotic string. We show how these couplings can be computed from closed string field theory. When the light fields we are interested in are charged under an underlying ${\mathcal N}=2$ $R$-charge in the left-moving sector, their quartic effective potential localizes at the boundary of the worldsheet moduli space, in complete analogy to the previously studied open string case. In particular we are able to compute the quartic closed string field theory potential without resorting to any explicit expression for the 3- and the 4-strings vertices but only using the $L_\infty$ relations between them. As a non trivial example we show how the heterotic Yang-Mills quartic potential arises in this way.

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arXiv2020

String Field Theory Solution for Any Open String Background. II

Generalizing previous work, we give a new analytic solution in Witten's open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE singularities. This requires leaving the familiar subalgebra of wedge states with insertions, but the payoff is that the solution makes no assumptions about the reference and target D-brane systems, and is therefore truly general. For example, unlike in previous work, the solution can describe time dependent backgrounds and multiple copies of the reference D-brane within the universal sector. The construction also resolves some subtle issues resulting from associativity anomalies, giving a more complete understanding of the relation between the degrees of freedom of different D-brane systems, and a nonperturbative proof of background independence in classical open bosonic string field theory.

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arXiv2019

Taming boundary condition changing operator anomalies with the tachyon vacuum

Motivated by the appearance of associativity anomalies in the context of superstring field theory, we give a generalized solution built from boundary condition changing operators which can be associated to a generic tachyon vacuum in the $KBc$ subalgebra of the Okawa form. We articulate sufficient conditions on the choice of tachyon vacuum to ensure that ambiguous products do not appear in the equations of motion.

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arXiv2019

Localization of effective actions in open superstring field theory: small Hilbert space

We consider the algebraic effective couplings for open superstring massless modes in the framework of the $A_\infty$ theory in the small Hilbert space. Focusing on quartic algebraic couplings, we reduce the effective action of the $A_\infty$ theory to the Berkovits one where we have already shown that such couplings are fully computed from contributions at the boundary of moduli space, when the massless fields under consideration are appropriately charged under an ${\cal N}\!=\!2$ $R$-symmetry. Here we offer a proof of localization which is in the small Hilbert space. We also discuss the flat directions of the obtained quartic potentials and give evidence for the existence of exactly marginal deformations in the $D3/D(-1)$ system in the framework of string field theory.

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