arXiv subjects

Daniele Bielli

Publications and source records attributed to Daniele Bielli.

17 recordsLinked to original sources

arXiv2026

The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin

The two-dimensional Breitenlohner-Maison (BM) model is a classically integrable subsector of $D=4$ general relativity endowed with two commuting Killing isometries, obtained via Kaluza-Klein reduction to $D=2$. Integrable deformations of such a theory have recently been constructed via auxiliary fields in the so-called $ν$-frame. In this work we first extend this point of view by deriving the complementary auxiliary field perspective known as $μ$-frame, and then explicitly construct the uplift to $D=4$ of both descriptions, relying on an ansatz inspired by duality-invariant Lagrangian formulations of Einstein theory. The resulting four-dimensional deformed model thus obtained is a higher-derivative theory which lacks manifest diffeomorphism invariance in both frames. We comment on possible resolutions of this puzzling feature and on the physical interpretation of the model in $D=4$.

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arXiv2026

The classical Yangian symmetry of Auxiliary Field Sigma Models

Integrable field theories exhibit infinitely many symmetries which underlie their solvability, but the structure of these symmetries can become obscured after performing an integrable deformation such as $\TT$ or an auxiliary field deformation. In this paper, we present a systematic organizing principle for understanding deformed charges and their Yangian structure in a broad class of integrable sigma models and their auxiliary field deformations. We generalize the recursive procedure of Brezin, Itzykson, Zinn-Justin, and Zuber (BIZZ) for generating non-local charges, and give sufficient conditions under which the resulting charges obey a Yangian algebra. We apply these results to many examples of integrable sigma models and their auxiliary field deformations, finding a Yangian algebra and Maillet bracket structure in all cases. This offers a unified explanation for the persistence of Hamiltonian integrability and Yangian symmetry across a wide landscape of deformed sigma models.

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arXiv2026

Relating auxiliary field formulations of $4d$ duality-invariant and $2d$ integrable field theories

Auxiliary field techniques have recently gained interest in four-dimensional non-linear electrodynamics and two-dimensional integrable sigma models. In these settings, coupling a suitable ``seed'' theory to auxiliary fields provides a powerful mechanism to generate infinite families of models while preserving key dynamical properties, such as electromagnetic duality invariance in four dimensions and classical integrability in two dimensions. Deformations induced through auxiliary fields are closely related to $T\bar{T}$-like deformations and, in two dimensions, also to their higher-spin generalisations. In this paper, we analyse and clarify the relations between different auxiliary field formulations in two and four dimensions, showing how they are governed by Legendre transformations of the interaction functions combined with appropriate field redefinitions. In four-dimensional electrodynamics, we establish a correspondence between the auxiliary field model of Russo and Townsend and the Ivanov--Zupnik formalism. In two dimensions, we develop the analogue of the Ivanov--Zupnik $μ$-frame to deform Principal Chiral, symmetric-space, non-Abelian T-dual, and (bi-)Yang-Baxter sigma models. We discuss how integrability is preserved and use properties of the $μ$-frame to further extend known families of integrable deformations.

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arXiv2025

Boundary Bethe ansatz in massive $AdS_3$

In this paper we perform the boundary algebraic Bethe Ansatz for massive representations of the $AdS_3 \times S^3 \times T^4$ integrable system. This is a companion analysis to our study of massless representations \cite{Bielli:2024bve}. Our treatment is comprehensive of all possible assortments of tensor-factor polarisations which build the physical representations in the spectrum, and includes different choices of auxiliary spaces, revealing subtle differences in the procedure. We survey both singlet and vector boundaries, obtaining the auxiliary Bethe equations in very general form for all cases.

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arXiv2025

Thin-wall vacuum decay in the presence of a compact dimension meets the $H_0$ and $S_8$ tensions

The proposal of a rapid sign-switching cosmological constant in the late universe, mirroring a transition from anti-de Sitter (AdS) to de Sitter (dS) space, has significantly improved the fit to observational data and provides a compelling framework for ameliorating major cosmological tensions, such as the $H_0$ and $S_8$ tensions. An attractive theoretical realisation that accommodates the AdS $\to$ dS transition relies on the Casimir forces of fields inhabiting the bulk of a 5-dimensional (5-dim) set up. Among the fields characterising the dark sector, there is a real scalar field $ϕ$ endowed with a potential holding two local minima with very small difference in vacuum energy and bigger curvature (mass) of the lower one. Shortly after the false vacuum tunnels to its true vacuum state, $ϕ$ becomes more massive and its contribution to the Casimir energy becomes exponentially suppressed. The tunneling process then changes the difference between the total number of fermionic and bosonic degrees of freedom contributing to the quantum corrections of the vacuum energy, yielding the AdS $\to$ dS transition. We investigate the properties of this theoretical realisation to validate its main hypothesis and characterise free parameters of the model. We adopt the Coleman-de Luccia formalism for calculating the transition probability within the thin-wall approximation. We show that the Euclidean bounce configuration that drives the transition between $ϕ$ vacua has associated at least a sixth order potential. We also show that distinctive features of the required vacuum decay to accommodate the AdS $\to$ dS transition are inconsistent with a 5-dim non-compact description of the instanton, for which the bounce is $O(5)$ symmetric, and instead call for a 5-dim instanton with a compact dimension, for which the bounce is $O(4)\times U(1)$ symmetric.

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arXiv2025

Higher-Spin Currents and Flows in Auxiliary Field Sigma Models

We study local, higher-spin conserved currents in integrable $2d$ sigma models that have been deformed via coupling to auxiliary fields. These currents generate integrability-preserving flows introduced by Smirnov and Zamolodchikov. For auxiliary field (AF) deformations of a free boson, we prove that local spin-$n$ currents exist for all $n$ and give recursion relations that characterize Smirnov-Zamolodchikov (SZ) flows driven by these currents. We then show how to construct spin-$2n$ currents in a unified class of auxiliary field sigma models with common structure -- including AF theories based on the principal chiral model (PCM), its non-Abelian T-dual, (bi-)Yang-Baxter deformations of the PCM, and symmetric space models -- for interaction functions of one variable, and describe SZ flows driven by any function of the stress tensor in these cases. Finally, we give perturbative solutions for spin-$3$ SZ flows in any member of our unified class of AF models with underlying $\mathfrak{su}(3)$ algebra. Part of our analysis shows that the class of AF deformations can be extended by allowing the interaction function to depend on a larger set of variables than has previously been considered.

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arXiv2024

Boundary Bethe ansatz in massless AdS3

We construct the boundary algebraic Bethe Ansatz for the AdS3 X S3 X T4 integrable reflection problem restricted to the massless sector. We derive the double-row monodromy and find the appropriate formulation of the dual equation of Sklyanin's. We perform the algebraic Bethe ansatz and obtain the RTT (more properly the RTRT) relations, from which the spectrum is obtained by repeated action of the B operator on the pseudovacuum. We obtain the Bethe equations by cancelling the unwanted terms, and prove the exact formulae for any number of quantum particles and magnonic excitations.

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arXiv2024

Auxiliary Field Sigma Models and Yang-Baxter Deformations

We combine the Yang-Baxter (YB) and bi-Yang-Baxter (bi-YB) deformations with higher-spin auxiliary field deformations to construct multi-parameter families of integrable deformations of the principal chiral model on a Lie group $G$ with semi-simple Lie algebra $\mathfrak{g}$. In the YB case, our construction produces one integrable deformation for each pair $(\mathcal{R}, E)$, where $\mathcal{R}$ is an antisymmetric bilinear operator on $\mathfrak{g}$ obeying the modified classical Yang-Baxter equation and $E$ is a function of several variables. In the bi-YB case, the pair becomes a triplet $(\mathcal{R},\tilde{\mathcal{R}}, E)$, where $\tilde{\mathcal{R}}$ is another antisymmetric bilinear operator on $\mathfrak{g}$ and obeys the non-split inhomogeneous modified classical Yang-Baxter equation. We show that every model in these families is (weakly) classically integrable by exhibiting a Lax representation for their equations of motion.

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arXiv2024

Thin-wall vacuum decay in the presence of a compact dimension

We study the problem of false vacuum decay in arbitrary dimensions, in the presence of gravity, and compute the transition probability within the thin-wall approximation, generalising the results of Coleman and de Luccia. In the particular case of one compact dimension, we present explicit formulae for the Euclidean Bounce configuration that drives the transition from a de Sitter to Minkowski or from a Minkowski to anti-de Sitter vacua.

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arXiv2024

Auxiliary Field Deformations of (Semi-)Symmetric Space Sigma Models

We generalize the auxiliary field deformations of the principal chiral model (PCM) introduced in arXiv:2405.05899 and arXiv:2407.16338 to sigma models whose target manifolds are symmetric or semi-symmetric spaces, including a Wess-Zumino term in the latter case. This gives rise to a new infinite family of classically integrable $\mathbb{Z}_2$ and $\mathbb{Z}_4$ coset models of the form which are of interest in applications of integrability to worldsheet string theory and holography. We demonstrate that every theory in this infinite class admits a zero-curvature representation for its equations of motion by exhibiting a Lax connection.

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arXiv2024

Integrable Higher-Spin Deformations of Sigma Models from Auxiliary Fields

We construct a new infinite family of integrable deformations of the principal chiral model (PCM) parameterized by an interaction function of several variables, which extends the formalism of arXiv:2405.05899, and includes deformations of the PCM by functions of both the stress tensor and higher-spin conserved currents. We show in detail that every model in this class admits a Lax representation for its equations of motion, and that the Poisson bracket of the Lax connection takes the Maillet form, establishing the existence of an infinite set of Poisson-commuting conserved charges. We argue that the non-Abelian T-dual of any model in this family is classically integrable, and that T-duality "commutes" with a general deformation in this class, in a sense which we make precise. Finally, we demonstrate that these higher-spin auxiliary field deformations can be extended to accommodate the addition of a Wess-Zumino term, and we exhibit the Lax connection in this case.

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arXiv2024

T-Duality and $T \overline{T}$-like Deformations of Sigma Models

We initiate the study of the interplay between T-duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T-duality commutes with the $T \overline{T}$ deformation, which can be engineered by a gravitational dressing. Then, by using an auxiliary field formulation of stress tensor deformations of the principal chiral model (PCM), we prove that non-Abelian T-duality and arbitrary $T \overline{T}$-like flows also commute for theories in this class. We argue that all such auxiliary field deformations of both the PCM and its T-dual are classically integrable.

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arXiv2024

Boundary scattering in massless $AdS_3$

We study the boundary integrability problem of the massless sector of $AdS_3 \times S^3 \times T^4 $ string theory. Exploiting the difference-form of the massless scattering theory, we find a very simple and exhaustive list of reflection matrices for all the possible boundary coideal subalgebras - singlet and vector representations, right and left boundary - and check basic properties of our solutions, primarily the boundary Yang-Baxter equation, for all possible combinations of scattering particles.

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arXiv2024

JT gravity from non-Abelian T-duality

We study the geometries obtained by performing super non-Abelian T-duality of the Principal Chiral Model on OSp$(1|2)$. While the initial model represents an appropriate 3D supergravity background, interpretable as the superspace version of AdS$_{3}$, the T-dual model fails solving the 3D supergravity torsion constraints. We argue that this has to do with a factorisation pattern taking place under dualisation: the dual 3D geometry can be rewritten as the supersymmetric version of AdS$_{2}$, satisfying the supergravity constraints, fibered over what we interpret as the superspace equivalent of the standard bosonic line. We discuss an interesting connection between T-duals of generic Principal Chiral Models and Poisson sigma models. We exploit it to show that in a suitable limit the dual action studied in this work gives rise to JT (super)gravity.

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arXiv2023

A study of integrable form factors in massless relativistic $AdS_2$

In this paper we initiate the study of form factors for the massless scattering of integrable $AdS_2$ superstrings, where the difference-form of the $S$-matrix can be exploited to implement the relativistic form factor bootstrap. The non-standard nature of the $S$-matrix implies that traditional methods do not apply. We use the fact that the massless $AdS_2$ $S$-matrix is a limit of a better-behaved $S$-matrix found by Fendley. We show that the previously conjectured massless $AdS_2$ dressing factor coincides with the limit of the De Martino - Moriconi improved dressing factor for the Fendley $S$-matrix. After finding a method to construct integral representations of relativistic dressing factors satisfying specific assumptions, we obtain analytic proofs of crossing and unitarity relations and propose a solution to the form factors constraints in the two-particle case.

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arXiv2022

On Super Non-Abelian T-Duality of Symmetric and Semi-Symmetric Coset Sigma Models

We review the algebraic approach to super non-Abelian T-Duality considered in [1], focusing on symmetric and semi-symmetric coset spaces on $G/H$. We discuss a potential impediment, appearing in these models when integrating out the gauge field in favour of the dual variables. This process cannot be performed in general and we isolate the obstruction, highlighting three cases in which a solution can be found. After writing the T-dual action we provide solution for two specific models. The first based on the symmetric space $S^{3} \simeq SO(4)/SO(3)$, well-known in the literature, the second on the semi-symmetric coset $OSp(1|2)/SO(1,1)$, a Green-Schwarz-like string sigma model satisfying the supergravity torsion constraints.

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arXiv2022

Super Non-Abelian T-Duality

We analyse super non-Abelian T-duality for principal chiral models, symmetric space sigma models, and semi-symmetric space sigma models for general Lie supergroups. This includes T-duality along both bosonic and fermionic directions. As an example, we perform the explicit dualisation of the OSp(1|2) principal chiral model, and, whilst the target superspace of this model is a three-dimensional supergravity background, we find that its super non-Abelian T-dual falls outside the class of such backgrounds.

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