arXiv subjects

Guido Macorini

Publications and source records attributed to Guido Macorini.

At least 19 recordsLinked to original sources

arXiv2021

Dynamics of a vortex lattice in an expanding polariton quantum fluid

If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantised vortices whose density is prescribed by the quantization of circulation. We report on the first experimental study of the Feynman-Onsager relation in a non-equilibrium polariton fluid, free to expand and rotate. Upon initially imprinting a lattice of vortices in the quantum fluid, we track the vortex core positions on picosecond time scales. We observe an accelerated stretching of the lattice and an outward bending of the linear trajectories of the vortices, due to the repulsive polariton interactions. Access to the full density and phase fields allows us to detect a small deviation from the Feynman-Onsager rule in terms of a transverse velocity component, due to the density gradient of the fluid envelope acting on the vortex lattice.

cond-mat.quant-gas↗

arXiv2020

Demonstration of dipolar-induced enhancement of parametric effects in polariton waveguides

Exciton-polaritons are hybrid light-matter excitations arising from the non-perturbative coupling of a photonic mode and an excitonic resonance. Behaving as interacting photons, they show optical third-order nonlinearities providing effects such as optical parametric oscillation or amplification. It has been suggested that polariton-polariton interactions can be greatly enhanced by inducing aligned electric dipoles in their excitonic part. However direct evidence of a true particle-particle interaction, such as superfluidity or parametric scattering is still missing. In this work, we demonstrate that dipolar interactions can be used to enhance parametric effects such as self-phase modulation in waveguide polaritons. By quantifying these optical nonlinearities we provide a reliable experimental measurement of the direct dipolar enhancement of polariton-polariton interactions.

physics.optics↗

arXiv2018

An evolutionary game model for behavioral gambit of loyalists: Global awareness and risk-aversion

We study the phase diagram of a minority game where three classes of agents are present. Two types of agents play a risk-loving game that we model by the standard Snowdrift Game. The behaviour of the third type of agents is coded by {\em indifference} w.r.t. the game at all: their dynamics is designed to account for risk-aversion as an innovative behavioral gambit. From this point of view, the choice of this solitary strategy is enhanced when innovation starts, while is depressed when it becomes the majority option. This implies that the payoff matrix of the game becomes dependent on the global awareness of the agents measured by the relevance of the population of the indifferent players. The resulting dynamics is non-trivial with different kinds of phase transition depending on a few model parameters. The phase diagram is studied on regular as well as complex networks.

physics.soc-ph↗

arXiv2017

Chiral trace relations in $Ω$-deformed $\mathcal N=2$ theories

We consider $\mathcal N=2$ $SU(2)$ gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic $Ω$-deformation. We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations. We predict exact relations valid at all instanton number among the traces $\langle\text{Tr}φ^{n}\rangle$, where $φ$ is the scalar field in the gauge multiplet. In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available quantized Seiberg-Witten curves. Instead, the full two-parameter deformation enjoys novel features and the ring relations require non trivial additional derivative terms with respect to the modular parameter. Higher rank groups are briefly discussed emphasizing non-factorization of correlators due to the $Ω$-deformation. Finally, the structure of the deformed ring relations in the $\mathcal N=2^{\star}$ theory is analyzed from the point of view of the Alday-Gaiotto-Tachikawa correspondence proving consistency as well as some interesting universality properties.

hep-th↗

arXiv2017

Reactive immunization on complex networks

Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel information across the network. On the other hand, static topological quantities measuring the connectivity structure are independent on the dynamical mechanisms of the infection. A natural question is therefore how to improve the topological analysis by some kind of dynamical information that may be extracted from the ongoing infection itself. In this spirit, we propose a novel vaccination scheme that exploits information from the details of the infection pattern at the moment when the vaccination strategy is applied. Numerical simulations of the infection process show that the proposed immunization strategy is effective and robust on a wide class of complex networks.

q-bio.PE↗

arXiv2016

Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_{f}=4$ flavours

We consider the $Ω$-deformed $\mathcal{N}=2$ $SU(2)$ gauge theory in four dimensions with $N_{f}=4$ massive fundamental hypermultiplets. The low energy effective action depends on the deformation parameters $\varepsilon_{1}, \varepsilon_{2}$, the scalar field expectation value $a$, and the hypermultiplet masses ${\bf m}=(m_{1}, m_{2}, m_{3}, m_{4})$. Motivated by recent findings in the $\mathcal{N}=2^{*}$ theory, we explore the theories that are characterized by special fixed ratios $\varepsilon_{2}/\varepsilon_{1}$ and ${\bf m}/\varepsilon_{1}$ and propose a simple condition on the structure of the multi-instanton contributions to the prepotential determining the effective action. This condition determines a finite set $Π_{N}$ of special points such that the prepotential has $N$ poles at fixed positions independent on the instanton number. In analogy with what happens in the $\mathcal{N}=2^{*}$ gauge theory, the full prepotential of the $Π_{N}$ theories may be given in closed form as an explicit function of $a$ and the modular parameter $q$ appearing in special combinations of Eisenstein series and Jacobi theta functions with well defined modular properties. The resulting finite pole partition functions are related by AGT correspondence to special 4-point spherical conformal blocks of the Virasoro algebra. We examine in full details special cases where the closed expression of the block is known and confirms our Ansatz. We systematically study the special features of Zamolodchikov's recursion for the $Π_{N}$ conformal blocks. As a result, we provide a novel effective recursion relation that can be exactly solved and allows to prove the conjectured closed expressions analytically in the case of the $Π_{1}$ and $Π_{2}$ conformal blocks.

hep-th↗

arXiv2016

Exact partition functions for the $Ω$-deformed $\mathcal N=2^{*}$ $SU(2)$ gauge theory

We study the low energy effective action of the $Ω$-deformed $\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $ε_{1},ε_{2}$, the scalar field expectation value $a$, and the hypermultiplet mass $m$. We explore the plane $(\frac{m}{ε_{1}}, \frac{ε_{2}}{ε_{1}})$ looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit $ε_{2}\to 0$. We propose a simple condition on the structure of poles of the $k$-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value $a$ and the modular parameter $q$ appearing in special combinations of Eisenstein series and Dedekind $η$ function. As a byproduct, the modular anomaly equation can be tested at all orders at these points. We discuss these special features from the point of view of the AGT correspondence and provide explicit toroidal 1-blocks in non-trivial closed form. The full list of solutions with 1, 2, 3, and 4 poles is determined and described in details.

hep-th↗

arXiv2016

On the cusp anomalous dimension in the ladder limit of $\mathcal N=4$ SYM

We analyze the cusp anomalous dimension in the (leading) ladder limit of $\mathcal N=4$ SYM and present new results for its higher-order perturbative expansion. We study two different limits with respect to the cusp angle $ϕ$. The first is the light-like regime where $x = e^{i\,ϕ}\to 0$. This limit is characterised by a non-trivial expansion of the cusp anomaly as a sum of powers of $\log x$, where the maximum exponent increases with the loop order. The coefficients of this expansion have remarkable transcendentality features and can be expressed by products of single zeta values. We show that the whole logarithmic expansion is fully captured by a solvable Woods-Saxon like one-dimensional potential. From the exact solution, we extract generating functions for the cusp anomaly as well as for the various specific transcendental structures appearing therein. The second limit that we discuss is the regime of small cusp angle. In this somewhat simpler case, we show how to organise the quantum mechanical perturbation theory in a novel efficient way by means of a suitable all-order Ansatz for the ground state of the associated Schrödinger problem. Our perturbative setup allows to systematically derive higher-order perturbative corrections in powers of the cusp angle as explicit non-perturbative functions of the effective coupling. This series approximation is compared with the numerical solution of the Schrödinger equation to show that we can achieve very good accuracy over the whole range of coupling and cusp angle. Our results have been obtained by relatively simple techniques. Nevertheless, they provide several non-trivial tests useful to check the application of Quantum Spectral Curve methods to the ladder approximation at non zero $ϕ$, in the two limits we studied.

hep-th↗

arXiv2015

Virasoro vacuum block at next-to-leading order in the heavy-light limit

We consider the semiclassical limit of the vacuum Virasoro block describing the diagonal 4-point correlation functions on the sphere. At large central charge c, after exponentiation, it depends on two fixed ratios h_H/c and h_L/c, where h_{H, L} are the conformal dimensions of the 4-point function operators. The semiclassical block may be expanded in powers of the light ratio h_L/c and the leading non-trivial (linear) order is known in closed form as a function of h_H/c. Recently, this contribution has been matched against AdS_3 gravity calculations where heavy operators build up a classical geometry corresponding to a BTZ black hole, while the light operators are described by a geodesic in this background. Here, we compute for the first time the next-to-leading quadratic correction O((h_L/c)^{2}), again in closed form for generic heavy operator ratio h_H/c. The result is a highly non-trivial extension of the leading order and may be relevant for further refined AdS_{3}/CFT_{2} tests. Applications to the two-interval Rényi entropy are also presented.

hep-th↗

arXiv2015

Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT

As was shown earlier, one-loop correction in 10d supergravity on AdS_5 x S^5 corresponds to the contributions to the vacuum energy and boundary 4d conformal anomaly which are minus the values for one n=4 Maxwell supermultiplet, thus reproducing the subleading term in their N^2-1 coefficient in the dual SU(N) SYM theory. We perform similar one-loop computations in 11d supergravity on AdS_7 x S^4 and 10d supergravity on AdS_3 x S^3 x T^4. In the AdS_7 case we find that the corrections to the 6d conformal anomaly a-coefficient and the vacuum energy are again minus the ones for one (2,0) tensor multiplet, suggesting that the total a-anomaly coefficient for the dual (2,0) theory is 4 N^3 - 9/4 N - 7/4 and thus vanishes for N=1. In the AdS_3 case the one-loop correction to the vacuum energy or 2d central charge turns out to be equal to that of one free (4,4) scalar multiplet, i.e. is c=+6. This reproduces the subleading term in the central charge c= 6(Q_1 Q_5 +1) of the dual 2d CFT describing decoupling limit of D5-D1 system. We also present the expressions for the 6d anomaly a-coefficient and vacuum energy for a general-symmetry higher spin field in AdS_7 and consider their application to tests of vectorial AdS/CFT with the boundary conformal 6d theory represented by free scalars, spinors or rank 2 antisymmetric tensors.

hep-th↗

arXiv2015

Higher Spin Lifshitz Theories and the KdV-Hierarchy

In this paper three dimensional higher spin theories in the Chern-Simons formulation with gauge algebra $sl(N,R)$ are investigated which have Lifshitz symmetry with scaling exponent $z$. We show that an explicit map exists for all $z$ and $N$ relating the Lifshitz Chern-Simons theory to the $(n,m)$ element of the KdV hierarchy. Furthermore we show that the map and hence the conserved charges are independent of $z$. We derive these result from the Drinfeld-Sokolov formalism of integrable systems.

hep-th↗

arXiv2014

On the one-loop curvature function in the $sl(2)$ sector of $\mathcal N=4$ SYM

We consider twist $J$ operators with spin $S$ in the $sl(2)$ sector of $\mathcal N=4$ SYM. The small spin expansion of their anomalous dimension defines the so-called slope functions. Much is known about the linear term, but the study of the quadratic correction, the curvature function, started only very recently. At any fixed $J$, the curvature function can be extracted at all loops from the $\mathbf{P}μ$-system formulation of the Thermodynamical Bethe Ansatz. Here, we work at the one-loop level and follow a different approach. We present a systematic double expansion of the Bethe Ansatz equations at large $J$ and small winding number. We succeed in fully resumming this expansion and obtain a closed explicit simple formula for the one-loop curvature function. The formula is parametric in $J$ and can be evaluated with minor effort for any fixed $J$. The result is an explicit series in odd-index $ζ$ values. Our approach provides a complete reconciliation between the $\mathbf{P}μ$-system predictions and the large $J$ approach.

hep-th↗

arXiv2014

Semiclassical folded string in AdS4 X CP3

We consider type IIA superstring theory on the background AdS4 x CP3, and the classical solution describing a folded string spinning in AdS4 with angular momentum in CP3. In the 't Hooft limit, it is the gravity dual of twist operators in the ABJM superconformal theory. We quantize the classical solution by algebraic curve methods and determine the first semiclassical correction to the energy. We provide an integral representation for this quantity valid for all values of the charges. We analyze its properties in the special regimes associated with a short or long string providing various accurate analytical expansions. Finally, we investigate various properties of the so-called slope, the leading term of the energy for short strings, collecting information that could be useful in attempts to generalize the exact results recently proposed for the folded string in AdS5 x S5.

hep-th↗

arXiv2014

On the next-to-leading holographic entanglement entropy in $AdS_{3}/CFT_{2}$

We reconsider the one-loop correction to the holographic entanglement entropy in $AdS_{3}/CFT_{2}$ by analysing the contributions due to a bulk higher spin $s$ current or a scalar field with scaling dimension $Δ$. We consider the two-interval case and work perturbatively in their small cross ratio $x$. We provide various results for the entanglement entropy due to the so-called CDW elements of the associated Schottky uniformization group. In particular, in the higher spin current case, we obtain a closed formula for all the contributions of the form $\mathcal O(x^{2s+p})$ up to $\mathcal O(x^{4s})$, where 2-CDW elements are relevant. In the scalar field case, we calculate the similar contributions for generic values of $Δ$. The terms up to $\mathcal O(x^{2Δ+5})$ are compared with an explicit CFT calculation with full agreement. The analysis exploits various simplifications which are valid in the strict entanglement limit of the Rényi entropy. This allows to identify in a clean way the relevant operators that provide the gravity result. The 2-CDW contributions are also analysed and a closed formula for the leading $\mathcal O(x^{4s})$ coefficient is presented as a function of the generic spin $s$. As a specific application, we combine the CDW and 2-CDW calculations and present the complete $\mathcal O(x^{4s+2})$ entanglement entropy for a spin $s=2,3,4$ higher spin current.

hep-th↗

arXiv2014

Analysis of higher spin black holes with spin-4 chemical potential

We consider the $AdS_{3}/CFT_{2}$ duality between certain coset WZW theories at large central charge and Vasiliev 3D higher spin gravity with a single complex field. On the gravity side, we discuss a higher spin black hole solution with chemical potential coupled to the spin-4 charge. We compute the perturbative expansion of the higher spin charges and of the partition function at high order in the chemical potential. The result is obtained with its exact dependence on the parameter $λ$ characterising the symmetry algebra $\mbox{hs}[λ]$. The cases of $λ=0,1$ are successfully compared with a CFT calculation. The special point $λ=\infty$, the Bergshoeff-Blencowe-Stelle limit, is also solved in terms of the exact generating function for the partition function. The thermodynamics of both the spin-4 and the usual spin-3 black holes is studied in order to discuss the $λ$ dependence of the BTZ critical temperature $T_{\rm BTZ}(λ)$. In the spin-3 case, it is shown that $T_{\rm BTZ}(λ)$ converges for large $λ$ to the critical point of the $λ=\infty$ known partition function previously found by the authors. In the spin-4 black hole, the picture is qualitatively similar and $T_{\rm BTZ}(\infty)$ is accurately determined by various numerical methods.

hep-th↗

arXiv2013

Resummation of scalar correlator in higher spin black hole background

We consider the proposal that predicts holographic duality between certain 2D minimal models at large central charge and Vasiliev 3D higher spin gravity with a single complex field. We compute the scalar correlator in the background of a higher spin black hole at order $\mathcal O(α^{5})$ in the chemical potential $α$ associated with the spin-3 charge. The calculation is performed at generic values of the symmetry algebra $\mbox{hs}[λ]$ parameter $λ$ and for the scalar in three different representations. We then study the perturbative data in the large $λ$ limit and discover remarkable regularities. This leads to formulate a closed formula for the resummation of the leading and subleading terms that scale like $\mathcal O(α^{n}λ^{2n})$ and $\mathcal O(α^{n}\,λ^{2n-1})$ respectively.

hep-th↗

arXiv2013

On the partition functions of higher spin black holes

We reconsider black hole solutions of D = 3 higher-spin gravity in the $hs[λ]\oplus hs[λ]$ Chern-Simons formulation. A suitable generalisation of the BTZ black hole has a spin-3 chemical potential $α$, and non-zero values of all the conserved charges associated with the asymptotic $\mathcal W_\infty[λ]$ symmetry. We extend the available perturbative expansion of the partition function to order $\mathcal O(α^{18})$ for generic values of the $λ$ parameter. The result matches the CFT prediction at $λ=0$ and at $λ=1$ where we provide the exact all-order expansion of the partition function. The perturbative series is then analysed in the interesting non-trivial limit $λ\to\infty$ and we derive the exact analytical expressions of the partition function and the spin-4 charge in closed form as functions of $α$. Also, the first subleading correction at large $λ$ is shown to be simply related to the leading contribution.

hep-th↗

arXiv2013

On a discrete symmetry of the Bremsstrahlung function in N=4 SYM

We consider the quark anti-quark potential on the three sphere in planar N=4 SYM and the associated vacuum potential in the near BPS limit with L units of R-charge. The associated Bremsstrahlung function B_L has been recently computed analytically by means of the Thermodynamical Bethe Ansatz. We discuss it at strong coupling by computing it at large but finite L. We provide strong support to a special symmetry of the Bremsstrahlung function under the formal discrete Z_2 symmetry L -> -1-L. In this context, it is the counterpart of the reciprocity invariance discovered in the past in the spectrum of various gauge invariant composite operators. The Z_2 symmetry has remarkable consequences in the scaling limit where L is taken to be large with fixed ratio to the 't Hooft coupling. This limit organizes in inverse powers of the coupling and resembles the semiclassical expansion of the dual string theory which is indeed known to capture the leading classical term. We show that the various higher-order contributions to the Bremsstrahlung function obey several constraints and, in particular, the next-to-leading term, formally associated with the string one-loop correction, is completely determined by the classical contribution. The large L limit at strong coupling is also discussed.

hep-th↗