arXiv subjects

Roberto Auzzi

Publications and source records attributed to Roberto Auzzi.

At least 19 recordsLinked to original sources

arXiv2026

Finite scalar field theory with SU(1,1) spacetime symmetry from near-BPS limits of $\mathcal{N}=4$ SYM

In this work, we consider an interacting and matrix-valued scalar quantum field theory that emerges from a near-BPS decoupling limit of $\mathcal{N}=4$ super Yang-Mills. The theory is non-Lorentzian with SU(1,1) spacetime symmetry and admits a (semi-)local action formulation. The interaction can be viewed as arising from a non-abelian gauge field without propagating degrees of freedom. The proposed field theory action has previously been considered as classically equivalent to SU(1,1) Spin Matrix theory. In this work, we examine this equivalence at the quantum level. We show that the classical action is off-shell invariant under the SU(1,1) symmetry group. We then analyze the renormalization properties, showing the theory is finite at all orders in perturbation theory. This provides a rare example of a non-supersymmetric and non-Lorentzian quantum field theory where a non-renormalization theorem holds.

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arXiv2026

Field Theory Models for a Holographic Superconductor in Two Dimensions

We investigate field theory models of holographic superconductors in which the condensation of the order parameter is induced by a Robin boundary condition. Assuming large-$c$ factorization, we study the phase diagram of a two-dimensional CFT deformed by a relevant double-trace perturbation. Using modular invariance, we relate the high- and low-temperature phases, reproducing analytically the results for the zero-winding sector of the holographic model. Moreover, we match the near-critical behaviour of the condensate with an effective Ginzburg--Landau field theory description. Another important feature of the holographic superconductor is the presence of vortices that carry fractional magnetic flux. We investigate a field theory toy model with similar properties and interpret it as a fractional Little--Parks effect.

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arXiv2025

Probing the bubble interior with entanglement entropy and bulk-cone singularities

In the thin wall approximation, we study a class of asymptotically AdS black holes which contain a spherically symmetric vacuum bubble with a different (positive or negative) cosmological constant. Collapsing, expanding, and static bubble solutions are considered. Among these, expanding bubbles with positive cosmological constant can provide a way to apply the AdS/CFT correspondence to describe the physics of an expanding universe. We systematically study the causal structure of the solutions as a function of the cosmological constant, the mass of the black hole, and the tension of the bubble. We then compute the holographic entanglement entropy for a class of boundary subregions using extremal codimension-two surfaces as a probe. For collapsing bubbles, we find examples in which the entanglement entropy also explores the geometry inside the black hole bifurcation surface. As a complementary way to probe the interior of the bubble, we investigate almost-null radial geodesics related to the bulk-cone singularities of boundary two-point correlators. While the bulk-cone singularities for collapsing and expanding bubbles are consistent with thermalization at late time, static bubbles violate thermalization and exhibit properties similar to those of scar states.

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arXiv2025

Solitonic vortices and black holes with vortex hair in AdS$_3$

We study soliton and black hole solutions with scalar hair in AdS$_3$ in a theory with a Maxwell field and a charged scalar field with double trace boundary conditions, which can trigger the dual boundary theory to become a superconductor. We investigate the phase diagram as a function of the temperature $T$ and of the double trace coupling $\kappa$ and we find a rich pattern of phase transitions, which can be of the Hawking-Page kind or can be due to the condensation of the order parameter. We also find a transition between vortex solutions and the zero temperature limit of the black hole for a critical value of the double trace coupling $\kappa$. The Little-Park periodicity is realized for the dual of the black hole solution with hair as a shift in the winding number and in the gauge field.

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arXiv2023

Volume complexity of dS bubbles

In the framework of the static patch approach to de Sitter holography introduced in [arXiv:2109.14104], the growth of holographic complexity has a hyperfast behaviour, which leads to a divergence in a finite time. This is very different from the AdS spacetime, where instead the complexity rate asymptotically reaches a constant value. We study holographic volume complexity in a class of asymptotically AdS geometries which include de Sitter bubbles in their interior. With the exception of the static bubble case, the complexity obtained from the volume of the smooth extremal surfaces which are anchored just to the AdS boundary has a similar behaviour to the AdS case, because it asymptotically grows linearly with time. The static bubble configuration has a zero complexity rate and corresponds to a discontinuous behaviour, which resembles a first order phase transition. If instead we consider extremal surfaces which are anchored at both the AdS boundary and the de Sitter stretched horizon, we find that complexity growth is hyperfast, as in the de Sitter case.

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arXiv2022

On the time dependence of holographic complexity for charged AdS black holes with scalar hair

In the presence of a scalar hair perturbation, the Cauchy horizon of a Reissner-Nordstr\"om black hole disappears and is replaced by the rapid collapse of the Einstein-Rosen bridge, which leads to a Kasner singularity [1,2]. We study the time-dependence of holographic complexity, both for the volume and for the action proposals, in a class of models with hairy black holes. Volume complexity can only probe a portion of the black hole interior that remains far away from the Kasner singularity. We provide numerical evidence that the Lloyd bound is satisfied by the volume complexity rate in all the parameter space that we explored. Action complexity can instead probe a portion of the spacetime closer to the singularity. In particular, the complexity rate diverges at the critical time $t_c$ for which the Wheeler-DeWitt patch touches the singularity. After the critical time the action complexity rate approaches a constant. We find that the Kasner exponent does not directly affect the details of the divergence of the complexity rate at $t=t_c$ and the late-time behaviour of the complexity. The Lloyd bound is violated by action complexity at finite time, because the complexity rate diverges at $t=t_c$. We find that the Lloyd bound is satisfied by the asymptotic action complexity rate in all the parameter space that we investigated.

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arXiv2021

Action complexity in the presence of defects and boundaries

The holographic complexity of formation for the AdS$_3$ $2$-sided Randall-Sundrum model and the AdS$_3$/BCFT$_2$ models is logarithmically divergent according to the volume conjecture, while it is finite using the action proposal. One might be tempted to conclude that the UV divergences of the volume and action conjectures are always different for defects and boundaries in two-dimensional conformal field theories. We show that this is not the case. In fact, in Janus AdS$_3$ we find that both volume and action proposals provide the same kind of logarithmic divergences.

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arXiv2021

A falling magnetic monopole as a holographic local quench

An analytic static monopole solution is found in global AdS$_4$, in the limit of small backreaction. This solution is mapped in Poincar\'e patch to a falling monopole configuration, which is dual to a local quench triggered by the injection of a condensate. Choosing boundary conditions which are dual to a time-independent Hamiltonian, we find the same functional form of the energy-momentum tensor as the one of a quench dual to a falling black hole. On the contrary, the details of the spread of entanglement entropy are very different from the falling black hole case where the quench induces always a higher entropy compared to the vacuum, i.e. $\Delta S >0$. In the propagation of entanglement entropy for the monopole quench, there is instead a competition between a negative contribution to $\Delta S$ due to the scalar condensate and a positive one carried by the freely propagating quasiparticles generated by the energy injection.

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arXiv2021

Volume complexity for Janus $\mathrm{AdS}_3$ geometries

We investigate the complexity=volume proposal in the case of Janus AdS$_3$ geometries, both at zero and finite temperature. The leading contribution coming from the Janus interface is a logarithmic divergence, whose coefficient is a function of the dilaton excursion. In the presence of the defect, complexity is no longer topological and becomes temperature-dependent. We also study the time evolution of the extremal volume for the time-dependent Janus BTZ black hole. This background is not dual to an interface but to a pair of entangled CFTs with different values of the couplings. At late times, when the equilibrium is restored, the couplings of the CFTs do not influence the complexity rate. On the contrary, the complexity rate for the out-of-equilibrium system is always smaller compared to the pure BTZ black hole background.

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arXiv2020

Geometry of quantum complexity

Computational complexity is a new quantum information concept that may play an important role in holography and in understanding the physics of the black hole interior. We consider quantum computational complexity for $n$ qubits using Nielsen's geometrical approach. We investigate a choice of penalties which, compared to previous definitions, increases in a more progressive way with the number of qubits simultaneously entangled by a given operation. This choice turns out to be free from singularities. We also analyze the relation between operator and state complexities, framing the discussion with the language of Riemannian submersions. This provides a direct relation between geodesics and curvatures in the unitaries and the states spaces, which we also exploit to give a closed-form expression for the metric on the states in terms of the one for the operators. Finally, we study conjugate points for a large number of qubits in the unitary space and we provide a strong indication that maximal complexity scales exponentially with the number of qubits in a certain regime of the penalties space.

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arXiv2019

On subregion action complexity in AdS$_3$ and in the BTZ black hole

We analytically compute subsystem action complexity for a segment in the BTZ black hole background up to the finite term, and we find that it is equal to the sum of a linearly divergent term proportional to the size of the subregion and of a term proportional to the entanglement entropy. This elegant structure does not survive to more complicated geometries: in the case of a two segments subregion in AdS$_3$, complexity has additional finite contributions. We give analytic results for the mutual action complexity of a two segments subregion.

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arXiv2019

The holographic vortex lattice using the circular cell method

We investigate vortex lattice solutions in a holographic superconductor model in asymptotically $AdS_4$ spacetime which includes the gravitational backreaction of the vortex. The circular cell approximation, which is known to give a good result for several physical quantities in the Ginzburg-Landau model, is used. The critical magnetic fields and the magnetization curve are computed. The vortex lattice profiles are compared to expectations from the Abrikosov solution in the regime nearby the upper critical magnetic field $H_{2c}$ for which superconductivity is lost.

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arXiv2019

On volume subregion complexity in Vaidya spacetime

We study holographic subregion volume complexity for a line segment in the AdS$_3$ Vaidya geometry. On the field theory side, this gravity background corresponds to a sudden quench which leads to the thermalization of the strongly-coupled dual conformal field theory. We find the time-dependent extremal volume surface by numerically solving a partial differential equation with boundary condition given by the Hubeny-Rangamani-Takayanagi surface, and we use this solution to compute holographic subregion complexity as a function of time. Approximate analytical expressions valid at early and at late times are derived.

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arXiv2019

Subsystem complexity in warped AdS

We compute the ultraviolet divergences of holographic subregion complexity for the left and right factors of the thermofield double state in warped AdS$_3$ black holes, both for the action and the volume conjectures. Besides the linear divergences, which are also present in the BTZ black hole, additional logarithmic divergences appear. For the action conjecture, these log divergences are not affected by the arbitrarity in the length scale associated with the counterterm needed to ensure reparameterization invariance. We find that the subregion action complexity obeys the superadditivity property for the thermofield double in warped AdS$_3$, independently from the action counterterm coefficient. We study the temperature dependence of subregion complexity at constant angular momentum and we find that it is correlated with the sign of the specific heat.

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arXiv2019

Renormalization properties of a Galilean Wess-Zumino model

We consider a Galilean N=2 supersymmetric theory in 2+1 dimensions with F-term couplings, obtained by null reduction of a relativistic Wess-Zumino model. We compute quantum corrections and we check that, as for the relativistic parent theory, the F-term does not receive quantum corrections. Even more, we find evidence that the causal structure of the non-relativistic dynamics together with particle number conservation constrain the theory to be one-loop exact.

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arXiv2019

The holographic non-abelian vortex

We study a fully back-reacted non-abelian vortex solution in an extension of the holographic superconductor setup. The thermodynamic properties of the vortex are computed. We show that, in some regime of parameters, the non-abelian vortex solution has a lower free energy than a competing abelian vortex solution. The solution is dual to a finite-temperature perturbed conformal field theory with a topological defect, on which operators related to the Goldstone modes of a spontaneously broken symmetry are localized. We compute numerically the retarded Green function of these operators and we find, in the classical approximation in the bulk, a gapless $\mathbb{CP}^1$ excitation on the vortex world line.

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arXiv2018

Complexity and action for warped AdS black holes

The Complexity=Action conjecture is studied for black holes in Warped AdS$_3$ space, realized as solutions of Einstein gravity plus matter. The time dependence of the action of the Wheeler-DeWitt patch is investigated, both for the non-rotating and the rotating case. The asymptotic growth rate is found to be equal to the Hawking temperature times the Bekenstein-Hawking entropy; this is in agreement with a previous calculation done using the Complexity=Volume conjecture.

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arXiv2018

Volume and complexity for warped AdS black holes

We study the Complexity=Volume conjecture for Warped AdS$_3$ black holes. We compute the spatial volume of the Einstein-Rosen bridge and we find that its growth rate is proportional to the Hawking temperature times the Bekenstein-Hawking entropy. This is consistent with expectations about computational complexity in the boundary theory.

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