Publications

Order by: publication date number of citations

• A comment on instantons and their fermion zero modes in adjoint QCD_2

  Andrei Smilga

  SciPost Phys. 10, 152 (2021) · published 22 June 2021 | Toggle abstract · pdf

  The adjoint 2-dimensional $QCD$ with the gauge group $SU(N)/Z_N$ admits topologically nontrivial gauge field configurations associated with nontrivial $\pi_1[SU(N)/Z_N] = Z_N$. The topological sectors are labelled by an integer $k=0,\ldots, N-1$. However, in contrast to $QED_2$ and $QCD_4$, this topology is not associated with an integral invariant like the magnetic flux or Pontryagin index. These instantons may admit fermion zero modes, but there is always an equal number of left-handed and right-handed modes, so that the Atiyah-Singer theorem, which determines in other cases the number of the modes, does not apply. The mod. 2 argument suggests that, for a generic gauge field configuration, there is either a single doublet of such zero modes or no modes whatsoever. However, the known solution of the Dirac problem for a wide class of gauge field configurations indicates the presence of $k(N-k)$ zero mode doublets in the topological sector $k$. In this note, we demonstrate in an explicit way that these modes are not robust under a generic enough deformation of the gauge background and confirm thereby the mod. 2 conjecture. The implications for the physics of this theory (screening vs. confinement issue) are briefly discussed.

  7 citations

• Natural boundaries for scattering amplitudes

  Sebastian Mizera

  SciPost Phys. 14, 101 (2023) · published 9 May 2023 | Toggle abstract · pdf

  Singularities, such as poles and branch points, play a crucial role in investigating the analytic properties of scattering amplitudes that inform new computational techniques. In this note, we point out that scattering amplitudes can also have another class of singularities called \emph{natural boundaries} of analyticity. They create a barrier beyond which analytic continuation cannot be performed. More concretely, we use unitarity to show that $2 \to 2$ scattering amplitudes in theories with a mass gap can have a natural boundary on the second sheet of the lightest threshold cut. There, an infinite number of ladder-type Landau singularities densely accumulates on the real axis in the center-of-mass energy plane. We argue that natural boundaries are generic features of higher-multiplicity scattering amplitudes in gapped theories.

  7 citations

• Semi-local Bounds on Null Energy in QFT

  Jackson R. Fliss, Ben Freivogel

  SciPost Phys. 12, 084 (2022) · published 7 March 2022 | Toggle abstract · pdf

  We investigate whether the null energy, averaged over some region of space- time, is bounded below in QFT. First, we use light-sheet quantization to prove a version of the “Smeared Null Energy Condition” (SNEC) proposed in [1], applicable for free and super-renormalizable QFT’s equipped with a UV cut- off. Through an explicit construction of squeezed states, we show that the SNEC bound cannot be improved by smearing on a light-sheet alone. We propose that smearing the null energy over two null directions defines an op- erator that is bounded below and independent of the UV cutoff, in what we call the “Double-Smeared Null Energy Condition,” or DSNEC. We indicate schematically how this bound behaves with respect to the smearing lengths and argue that the DSNEC displays a transition when the smearing lengths are comparable to the correlation length.

  7 citations

• Boundary modes in the Chamon model

  Weslei B. Fontana, Rodrigo G. Pereira

  SciPost Phys. 15, 010 (2023) · published 17 July 2023 | Toggle abstract · pdf

  We study the fracton phase described by the Chamon model in a manifold with a boundary. The new processess and excitations emerging at the boundary can be understood by means of a diagrammatic framework. From a continuum perspective, the boundary theory is described by a set of scalar fields in similarity with standard $K$-matrix Chern-Simons theory. The continuum theory recovers the gapped boundaries of the lattice model once we include sufficiently strong interactions that break charge conservation. The analysis of the perturbative relevance of the leading interactions reveals a regime in which the Chamon model can have a stable gapless fractonic phase at its boundary.

  7 citations

• Quantum hypothesis testing in many-body systems

  Jan de Boer, Victor Godet, Jani Kastikainen, Esko Keski-Vakkuri

  SciPost Phys. Core 4, 019 (2021) · published 23 June 2021 | Toggle abstract · pdf

  One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the system in state A or state B?". In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.

  7 citations

• Electrostatic solution of massless quenches in Luttinger liquids

  Paola Ruggiero, Pasquale Calabrese, Thierry Giamarchi, Laura Foini

  SciPost Phys. 13, 111 (2022) · published 18 November 2022 | Toggle abstract · pdf

  The study of non-equilibrium dynamics of many-body systems after a quantum quench received a considerable boost and a deep theoretical understanding from the path integral formulation in imaginary time. However, the celebrated problem of a quench in the Luttinger parameter of a one dimensional quantum critical system (massless quench) has so far only been solved in the real-time Heisenberg picture. In order to bridge this theoretical gap and to understand on the same ground massive and massless quenches, we study the problem of a gaussian field characterized by a coupling parameter $K$ within a strip and a different one $K_0$ in the remaining two semi-infinite planes. We give a fully analytical solution using the electrostatic analogy with the problem of a dielectric material within a strip surrounded by an infinite medium of different dielectric constant, and exploiting the method of charge images. After analytic continuation, this solution allows us to obtain all the correlation functions after the quench within a path integral approach in imaginary time, thus recovering and generalizing the results in real time. Furthermore, this imaginary-time approach establishes a remarkable connection between the quench and the famous problem of the conductivity of a Tomonaga-Luttinger liquid coupled to two semi-infinite leads: the two are in fact related by a rotation of the spacetime coordinates.

  6 citations

• Electric conductivity in non-Hermitian holography

  Zhuo-Yu Xian, David Rodríguez Fernández, Zhaohui Chen, Yang Liu, René Meyer

  SciPost Phys. 16, 004 (2024) · published 5 January 2024 | Toggle abstract · pdf

  We study the phase structure and charge transport at finite temperature and chemical potential in the non-Hermitian $\mathcal{PT}$-symmetric holographic model of [SciPost Phys. 9, 032 (2020)]. The non-Hermitian $\mathcal{PT}$-symmetric deformation is realized by promoting the parameter of a global U(1) symmetry to a complex number. Depending on the strength of the deformation, we find three phases: stable $\mathcal{PT}$-symmetric phase, unstable $\mathcal{PT}$-symmetric phase, and an unstable $\mathcal{PT}$-symmetry broken phase. In the three phases, the square of the condensate and also the spectral weight of the AC conductivity at zero frequency are, respectively, positive, negative, and complex. We check that the Ferrell-Glover-Tinkham sum rule for the AC conductivity holds in all the three phases. We also investigate a complexified U(1) rotor model with $\mathcal{PT}$-symmetric deformation, derive its phase structure and condensation pattern, and find a zero frequency spectral weight analogous to the holographic model.

  6 citations

• Symmetries versus the spectrum of $ J\bar T$-deformed CFTs

  Monica Guica

  SciPost Phys. 10, 065 (2021) · published 11 March 2021 | Toggle abstract · pdf

  It has been recently shown that classical $J\bar T$ - deformed CFTs possess an infinite-dimensional Witt-Ka\v{c}-Moody symmetry, generated by certain field-dependent coordinate and gauge transformations. On a cylinder, however, the equal spacing of the descendants' energies predicted by such a symmetry algebra is inconsistent with the known finite-size spectrum of $J\bar T$ - deformed CFTs. Also, the associated quantum symmetry generators do not have a proper action on the Hilbert space. In this article, we resolve this tension by finding a new set of (classical) conserved charges, whose action is consistent with semi-classical quantization, and which are related to the previous symmetry generators by a type of energy-dependent spectral flow. The previous inconsistency between the algebra and the spectrum is resolved because the energy operator does not belong to the spectrally flowed sector.

  6 citations

• Conformal boundary conditions for a 4d scalar field

  Lorenzo Di Pietro, Edoardo Lauria, Pierluigi Niro

  SciPost Phys. 16, 090 (2024) · published 3 April 2024 | Toggle abstract · pdf

  We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$ with $N_f$ flavors and a Chern-Simons term at level $k$, in the large-$N_f$ limit with fixed $k/N_f$. We find that interacting boundary conditions only exist when $k≠ 0$. To obtain this result we compute the $\beta$ functions of the classically marginal couplings at the first non-vanishing order in the large-$N_f$ expansion, and to all orders in $k/N_f$ and in the couplings. To check vacuum stability we also compute the large-$N_f$ effective potential. We compare our results with the the known conformal bootstrap bounds.

  6 citations

• From combinatorial maps to correlation functions in loop models

  Linnea Grans-Samuelsson, Jesper Lykke Jacobsen, Rongvoram Nivesvivat, Sylvain Ribault, Hubert Saleur

  SciPost Phys. 15, 147 (2023) · published 9 October 2023 | Toggle abstract · pdf

  In two-dimensional statistical physics, correlation functions of the $O(N)$ and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as ribbon graphs). We allow disconnected maps, but not maps that include monogons. Given a map with $n$ vertices, we obtain a function of the moduli of the corresponding punctured Riemann surface. Due to the map's combinatorial (rather than topological) nature, that function is single-valued, and we call it an $n$-point correlation function. We conjecture that in the critical limit, such functions form a basis of solutions of certain conformal bootstrap equations. They include all correlation functions of the $O(N)$ and Potts models, and correlation functions that do not belong to any known model. We test the conjecture by counting solutions of crossing symmetry for four-point functions on the sphere.

  6 citations