Riccardo Borsato
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Riccardo Borsato has a total of 27 co-authors. Here are the top co-authors by number of shared publications:
- Alessandro Sfondrini
University of Birmingham
18 shared publications - Linus Wulff
Masaryk University
17 shared publications - Olof Ohlsson Sax
Nordita, Stockholm University and KTH Royal Institute of Technology
17 shared publications - Bogdan Stefański
University of London
11 shared publications - Sibylle Driezen
ETH Zurich
10 shared publications - Alessandro Torrielli
University of Surrey
9 shared publications
Latest Publications
- Open Access
- 27 May 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (5) , 309
Non-commutative deformations of gauge theories via Drinfel’d twists of the scale symmetry
A bstract: In this paper we consider gauge theories that are relativistic and scale-invariant, and we construct their deformed versions via suitable star products. In particular, the non-commutative structure is controlled by Drinfel’d twists that are built out of symmetry generators that include the scale transformation. To achieve this, we construct a twisted differential calculus that allows us to identify the proper gauge-covariant quantities. We also show that our construction is equivalent to twists where the symmetry generators are implemented as active transformations of fields. As a consequence of our construction, the deformed gauge theories possess a twisted version of the original symmetry group. Moreover, at the planar level, the deformation is encoded just on the external legs of Feynman diagrams, leaving then the amputated diagrams undeformed. This work extends previous constructions and allows us to define twist-deformations of $$ \mathcal{N}=4 $$ super Yang-Mills that are conjectured to be holographically dual to a class of homogeneous Yang-Baxter deformations of AdS 5 × S 5 .- 27 May 2026
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2026 (5) , 309
Open AccessNon-commutative deformations of gauge theories via Drinfel’d twists of the scale symmetry
A bstract: In this paper we consider gauge theories that are relativistic and scale-invariant, and we construct their deformed versions via suitable star products. In particular, the non-commutative structure is controlled by Drinfel’d twists that are built out of symmetry generators that include the scale transformation. To achieve this, we construct a twisted differential calculus that allows us to identify the proper gauge-covariant quantities. We also show that our construction is equivalent to twists where the symmetry generators are implemented as active transformations of fields. As a consequence of our construction, the deformed gauge theories possess a twisted version of the original symmetry group. Moreover, at the planar level, the deformation is encoded just on the external legs of Feynman diagrams, leaving then the amputated diagrams undeformed. This work extends previous constructions and allows us to define twist-deformations of $$ \mathcal{N}=4 $$ super Yang-Mills that are conjectured to be holographically dual to a class of homogeneous Yang-Baxter deformations of AdS 5 × S 5 . - Open Access
Non-commutative deformations of gauge theories via Drinfel'd twists of the scale symmetry
In this paper we consider gauge theories that are relativistic and scale-invariant, and we construct their deformed versions via suitable star products. In particular, the non-commutative structure is controlled by Drinfel'd twists that are built out of symmetry generators that include the scale transformation. To achieve this, we construct a twisted differential calculus that allows us to identify the proper gauge-covariant quantities. We also show that our construction is equivalent to twists where the symmetry generators are implemented as active transformations of fields. As a consequence of our construction, the deformed gauge theories possess a twisted version of the original symmetry group. Moreover, at the planar level, the deformation is encoded just on the external legs of Feynman diagrams, leaving then the amputated diagrams undeformed. This work extends previous constructions and allows us to define twist-deformations of $\mathcal N=4$ super Yang-Mills that are conjectured to be holographically dual to a class of homogeneous Yang-Baxter deformations of $AdS_5\times S^5$.Open AccessNon-commutative deformations of gauge theories via Drinfel'd twists of the scale symmetry
In this paper we consider gauge theories that are relativistic and scale-invariant, and we construct their deformed versions via suitable star products. In particular, the non-commutative structure is controlled by Drinfel'd twists that are built out of symmetry generators that include the scale transformation. To achieve this, we construct a twisted differential calculus that allows us to identify the proper gauge-covariant quantities. We also show that our construction is equivalent to twists where the symmetry generators are implemented as active transformations of fields. As a consequence of our construction, the deformed gauge theories possess a twisted version of the original symmetry group. Moreover, at the planar level, the deformation is encoded just on the external legs of Feynman diagrams, leaving then the amputated diagrams undeformed. This work extends previous constructions and allows us to define twist-deformations of $\mathcal N=4$ super Yang-Mills that are conjectured to be holographically dual to a class of homogeneous Yang-Baxter deformations of $AdS_5\times S^5$. - Open Access
- 12 August 2025
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2025 (8) , 1-56
Jordanian deformation of the non-compact and $ \mathfrak{s}{\mathfrak{l}}_2 $-invariant XXX−1/2 spin-chainUsing a Drinfeld twist of Jordanian type, we construct a deformation of the non-compact and $$ \mathfrak{s}{\mathfrak{l}}_2 $$ -invariant XXX −1/2 spin-chain. Before the deformation, the seed model can be understood as a sector of the $$ \mathfrak{psu} $$ (2, 2|4)-invariant spin-chain encoding the spectral problem of $$ \mathcal{N} $$ = 4 super Yang-Mills at one loop in the planar limit. The deformation gives rise to interesting features because, while being integrable, the Hamiltonian is non-hermitian and non-diagonalisable, so that it only admits a Jordan decomposition. Moreover, the eigenvalues of the deformed Hamiltonian coincide with those of the original undeformed spin-chain. We use explicit examples as well as the techniques of the coordinate and of the algebraic Bethe ansatz to discuss the construction of the (generalised) eigenvectors of the deformed model. We also show that the deformed spin-chain is equivalent to an undeformed one with twisted boundary conditions, and that it may be derived from a scaling limit of the non-compact U q ( $$ \mathfrak{s}{\mathfrak{l}}_2 $$ )-invariant XXZ −1/2 spin-chain.- 12 August 2025
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2025 (8) , 1-56
Open AccessJordanian deformation of the non-compact and $ \mathfrak{s}{\mathfrak{l}}_2 $-invariant XXX−1/2 spin-chainUsing a Drinfeld twist of Jordanian type, we construct a deformation of the non-compact and $$ \mathfrak{s}{\mathfrak{l}}_2 $$ -invariant XXX −1/2 spin-chain. Before the deformation, the seed model can be understood as a sector of the $$ \mathfrak{psu} $$ (2, 2|4)-invariant spin-chain encoding the spectral problem of $$ \mathcal{N} $$ = 4 super Yang-Mills at one loop in the planar limit. The deformation gives rise to interesting features because, while being integrable, the Hamiltonian is non-hermitian and non-diagonalisable, so that it only admits a Jordan decomposition. Moreover, the eigenvalues of the deformed Hamiltonian coincide with those of the original undeformed spin-chain. We use explicit examples as well as the techniques of the coordinate and of the algebraic Bethe ansatz to discuss the construction of the (generalised) eigenvectors of the deformed model. We also show that the deformed spin-chain is equivalent to an undeformed one with twisted boundary conditions, and that it may be derived from a scaling limit of the non-compact U q ( $$ \mathfrak{s}{\mathfrak{l}}_2 $$ )-invariant XXZ −1/2 spin-chain. - Open Access
- 9 April 2025
- Published by American Physical Society (APS) in Physical Review D
- Vol. 111 (8)
Particle production in a light-cone gauge fixed Jordanian deformation ofWe consider a string on a Jordanian deformation of the AdS 5 × S 5 spacetime. This model belongs to the larger class of homogeneous Yang-Baxter deformations, which preserve classical integrability in the sense that one can construct an explicit Lax connection. To study the scattering of bosonic worldsheet excitations, we fix light-cone gauge and expand around a pointlike classical solution that reduces to the BMN vacuum in the undeformed limit. Our analysis shows that the light-cone gauge-fixed Hamiltonian, under a perturbative field expansion, includes cubic terms that give rise to nontrivial cubic processes for physical particles. We discuss this unexpected result in relation to the property of Lax integrability of the sigma-model.
- 9 April 2025
- Published by American Physical Society (APS) in Physical Review D
- Vol. 111 (8)
Open AccessParticle production in a light-cone gauge fixed Jordanian deformation ofWe consider a string on a Jordanian deformation of the AdS 5 × S 5 spacetime. This model belongs to the larger class of homogeneous Yang-Baxter deformations, which preserve classical integrability in the sense that one can construct an explicit Lax connection. To study the scattering of bosonic worldsheet excitations, we fix light-cone gauge and expand around a pointlike classical solution that reduces to the BMN vacuum in the undeformed limit. Our analysis shows that the light-cone gauge-fixed Hamiltonian, under a perturbative field expansion, includes cubic terms that give rise to nontrivial cubic processes for physical particles. We discuss this unexpected result in relation to the property of Lax integrability of the sigma-model.
- Open Access
- 14 March 2025
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2025 (3) , 1-38
Integrability of the λ-deformation of the PCM with spectators
We construct a generalisation of the λ-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup F of the full symmetry group G. We find that demanding Lax integrability imposes a crucial restriction, namely that the coset F\G must be symmetric. Surprisingly, we also find that (when F is non-abelian) integrability requires that the term in the action involving only the spectator fields should have a specific λ-dependence, which is a curious modification of the procedure expected from the known F = G case. The resulting Lax connection has a novel analytical structure, with four single poles as opposed to the two poles of the cases of the PCM and of the standard λ-deformation. We also explicitly work out the example of G = SU(2) and F = U(1), discussing its renormalisation group flow to two loops.
- 14 March 2025
- Published by Springer Nature in Journal of High Energy Physics
- Vol. 2025 (3) , 1-38
Open AccessIntegrability of the λ-deformation of the PCM with spectators
We construct a generalisation of the λ-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup F of the full symmetry group G. We find that demanding Lax integrability imposes a crucial restriction, namely that the coset F\G must be symmetric. Surprisingly, we also find that (when F is non-abelian) integrability requires that the term in the action involving only the spectator fields should have a specific λ-dependence, which is a curious modification of the procedure expected from the known F = G case. The resulting Lax connection has a novel analytical structure, with four single poles as opposed to the two poles of the cases of the PCM and of the standard λ-deformation. We also explicitly work out the example of G = SU(2) and F = U(1), discussing its renormalisation group flow to two loops.
- Top Cited PapersOpen Access
- 26 June 2024
- Published by Springer Nature in The European Physical Journal C
- Vol. 84 (6) , 1-41
Lecture notes on current–current deformations
These are pedagogical lecture notes discussing current–current deformations of 2-dimensional field theories. The deformations that are considered here are generated infinitesimally by bilinears of Noether currents corresponding to internal global symmetries of the “seed” theory. When the seed theory is conformal, these deformations are marginal and are often known as $$J{\bar{J}}$$ -deformations. In this context, we review the criterion for marginal operators due to Chaudhuri and Schwartz. When the seed theory is an integrable $$\sigma $$ -model (in the sense that it possesses a Lax connection), these deformations preserve the integrability. Here we review this fact by viewing the deformations as maps that leave the equations of motion and the Poisson brackets of the 2-dimensional $$\sigma $$ -models invariant. The reinterpretation as undeformed theories with twisted boundary conditions is also discussed, as well as the effect of the deformation at the level of the S-matrix of the quantum theory. The finite (or integrated) form of the deformations is equivalent to sequences of T-duality–shift–T-duality transformations (TsT’s), and here we review the O(d, d)-covariant formalism that is useful to describe them. The presentation starts with pedagogical examples of deformations of free massless scalars in 2 dimensions, and minimal prerequisites on conformal field theories or integrability are needed to understand later sections. Moreover, guided exercises are proposed to the reader. These notes were prepared for the Young Researchers Integrability School and Workshop (YRISW) held in Durham from 17 to 21 July 2023.- 26 June 2024
- Published by Springer Nature in The European Physical Journal C
- Vol. 84 (6) , 1-41
Top Cited PapersOpen AccessLecture notes on current–current deformations
These are pedagogical lecture notes discussing current–current deformations of 2-dimensional field theories. The deformations that are considered here are generated infinitesimally by bilinears of Noether currents corresponding to internal global symmetries of the “seed” theory. When the seed theory is conformal, these deformations are marginal and are often known as $$J{\bar{J}}$$ -deformations. In this context, we review the criterion for marginal operators due to Chaudhuri and Schwartz. When the seed theory is an integrable $$\sigma $$ -model (in the sense that it possesses a Lax connection), these deformations preserve the integrability. Here we review this fact by viewing the deformations as maps that leave the equations of motion and the Poisson brackets of the 2-dimensional $$\sigma $$ -models invariant. The reinterpretation as undeformed theories with twisted boundary conditions is also discussed, as well as the effect of the deformation at the level of the S-matrix of the quantum theory. The finite (or integrated) form of the deformations is equivalent to sequences of T-duality–shift–T-duality transformations (TsT’s), and here we review the O(d, d)-covariant formalism that is useful to describe them. The presentation starts with pedagogical examples of deformations of free massless scalars in 2 dimensions, and minimal prerequisites on conformal field theories or integrability are needed to understand later sections. Moreover, guided exercises are proposed to the reader. These notes were prepared for the Young Researchers Integrability School and Workshop (YRISW) held in Durham from 17 to 21 July 2023. - Open Access
- 30 May 2024
- Published by American Physical Society (APS) in Physical Review D
- Vol. 109 (10) , 106023
Inequivalent light-cone gauge-fixings of strings on backgroundsLight-cone gauge-fixed sigma models on backgrounds play an important role in the integrability formulation of the correspondence. The string spectrum of the sigma model is gauge independent, however the Hamiltonian and scattering matrix of the transverse world sheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as , , , and deformations. We investigate the moduli space of inequivalent light-cone gauges and, specializing to , compute the different light-cone gauge symmetry algebras, well known to be for the standard gauge-fixing. Many integrable deformations require a nonstandard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analyzing such models.- 30 May 2024
- Published by American Physical Society (APS) in Physical Review D
- Vol. 109 (10) , 106023
Open AccessInequivalent light-cone gauge-fixings of strings on backgroundsLight-cone gauge-fixed sigma models on backgrounds play an important role in the integrability formulation of the correspondence. The string spectrum of the sigma model is gauge independent, however the Hamiltonian and scattering matrix of the transverse world sheet fields are not. We study how these change for a large family of inequivalent light-cone gauges, which are interpreted as , , , and deformations. We investigate the moduli space of inequivalent light-cone gauges and, specializing to , compute the different light-cone gauge symmetry algebras, well known to be for the standard gauge-fixing. Many integrable deformations require a nonstandard light-cone gauge, hence our classification and analysis of inequivalent gauges will be important for analyzing such models. - Open Access
- 19 June 2023
- Published by Stichting SciPost in SciPost Physics
- Vol. 14 (6) , 160
All Jordanian deformations of the $AdS_5 \times S^5$ superstringWe explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on \mathfrak{psu}(2,2|4) ???? ???? ???? ( 2 , 2 | 4 ) , corresponding to Jordanian Yang-Baxter deformations of the AdS_5\times S^5 A d S 5 × S 5 superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number N<32 of supercharges that can be N=12,8,6,4,0.
- 19 June 2023
- Published by Stichting SciPost in SciPost Physics
- Vol. 14 (6) , 160
Open AccessAll Jordanian deformations of the $AdS_5 \times S^5$ superstringWe explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on \mathfrak{psu}(2,2|4) ???? ???? ???? ( 2 , 2 | 4 ) , corresponding to Jordanian Yang-Baxter deformations of the AdS_5\times S^5 A d S 5 × S 5 superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number N<32 of supercharges that can be N=12,8,6,4,0.
- Open AccessAll Jordanian deformations of the $AdS_5 \times S^5$ superstringWe explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on $\mathfrak{psu}(2,2|4)$, corresponding to Jordanian Yang-Baxter deformations of the $AdS_5\times S^5$ superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number $N<32$ of supercharges that can be $N=12,8,6,4,0$.Open AccessAll Jordanian deformations of the $AdS_5 \times S^5$ superstringWe explicitly construct and classify all Jordanian solutions of the classical Yang-Baxter equation on $\mathfrak{psu}(2,2|4)$, corresponding to Jordanian Yang-Baxter deformations of the $AdS_5\times S^5$ superstring. Such deformations preserve the classical integrability of the underlying sigma-model and thus are a subclass of all possible integrable deformations. The deformations that we consider are divided into two families, unimodular and non-unimodular ones. The former ensure that the deformed backgrounds are still solutions of the type IIB supergravity equations. For the simplest unimodular solutions, we find that the corresponding backgrounds preserve a number $N<32$ of supercharges that can be $N=12,8,6,4,0$.
- Open AccessSemiclassical spectrum of a Jordanian deformation of $AdS_5 \times S^5$We study a Jordanian deformation of the $AdS_5 \times S^5$ superstring that preserves 12 superisometries. It is an example of homogeneous Yang-Baxter deformations, a class that generalises TsT deformations to the non-abelian case. Many of the attractive features of TsT carry over to this more general class, from the possibility of generating new supergravity solutions to the preservation of worldsheet integrability. In this paper, we exploit the fact that the deformed $\sigma$-model with periodic boundary conditions can be reformulated as an undeformed one with twisted boundary conditions, to discuss the construction of the classical spectral curve and its semi-classical quantisation. First, we find global coordinates for the deformed background, and identify the global time corresponding to the energy that should be computed in the spectral problem. Using the curve of the twisted model, we obtain the one-loop correction to the energy of a particular solution, and we find that the charge encoding the twisted boundary conditions does not receive an anomalous correction. Finally, we give evidence suggesting that the unimodular version of the deformation (giving rise to a supergravity background) and the non-unimodular one (whose background does not solve the supergravity equations) have the same spectrum at least to one-loop.Open AccessSemiclassical spectrum of a Jordanian deformation of $AdS_5 \times S^5$We study a Jordanian deformation of the $AdS_5 \times S^5$ superstring that preserves 12 superisometries. It is an example of homogeneous Yang-Baxter deformations, a class that generalises TsT deformations to the non-abelian case. Many of the attractive features of TsT carry over to this more general class, from the possibility of generating new supergravity solutions to the preservation of worldsheet integrability. In this paper, we exploit the fact that the deformed $\sigma$-model with periodic boundary conditions can be reformulated as an undeformed one with twisted boundary conditions, to discuss the construction of the classical spectral curve and its semi-classical quantisation. First, we find global coordinates for the deformed background, and identify the global time corresponding to the energy that should be computed in the spectral problem. Using the curve of the twisted model, we obtain the one-loop correction to the energy of a particular solution, and we find that the charge encoding the twisted boundary conditions does not receive an anomalous correction. Finally, we give evidence suggesting that the unimodular version of the deformation (giving rise to a supergravity background) and the non-unimodular one (whose background does not solve the supergravity equations) have the same spectrum at least to one-loop.