Publications

Order by: publication date number of citations

• Perturbative and nonperturbative studies of CFTs with MN global symmetry

  Johan Henriksson, Andreas Stergiou

  SciPost Phys. 11, 015 (2021) · published 16 July 2021 | Toggle abstract · pdf

  Fixed points in three dimensions described by conformal field theories with $MN_{m,n}= O(m)^n\rtimes S_n$ global symmetry have extensive applications in critical phenomena. Associated experimental data for $m=n=2$ suggest the existence of two non-trivial fixed points, while the $\varepsilon$ expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters $m$ and $n$, with critical exponents in good agreement with experimental determinations in the $m=n=2$ case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters $m$ and $n$. We find that one family of kinks approaches a perturbative limit as $m$ increases, and using large spin perturbation theory we construct a large $m$ expansion that fits well with the numerical data. This new expansion, akin to the large $N$ expansion of critical $O(N)$ models, is compatible with the fixed point found in the $\varepsilon$ expansion. For the other family of kinks, we find that it persists only for $n=2$, where for large $m$ it approaches a non-perturbative limit with $\Delta_\phi\approx 0.75$. We investigate the spectrum in the case $MN_{100,2}$ and find consistency with expectations from the lightcone bootstrap.

  17 citations

• Yangian bootstrap for massive Feynman integrals

  Florian Loebbert, Julian Miczajka, Dennis Müller, Hagen Münkler

  SciPost Phys. 11, 010 (2021) · published 13 July 2021 | Toggle abstract · pdf

  We extend the study of the recently discovered Yangian symmetry of massive Feynman integrals and its relation to massive momentum space conformal symmetry. After proving the symmetry statements in detail at one and two loop orders, we employ the conformal and Yangian constraints to bootstrap various one-loop examples of massive Feynman integrals. In particular, we explore the interplay between Yangian symmetry and hypergeometric expressions of the considered integrals. Based on these examples we conjecture single series representations for all dual conformal one-loop integrals in $D$ spacetime dimensions with generic massive propagators.

  15 citations

• EFT and the SUSY index on the 2nd sheet

  Davide Cassani, Zohar Komargodski

  SciPost Phys. 11, 004 (2021) · published 9 July 2021 | Toggle abstract · pdf

  The counting of BPS states in four-dimensional ${\cal N}=1$ theories has attracted a lot of attention in recent years. For superconformal theories, these states are in one-to-one correspondence with local operators in various short representations. The generating function for this counting problem has branch cuts and hence several Cardy-like limits, which are analogous to high-temperature limits. Particularly interesting is the second sheet, which has been shown to capture the microstates and phases of supersymmetric black holes in AdS$_5$. Here we present a 3d Effective Field Theory (EFT) approach to the high-temperature limit on the second sheet. We use the EFT to derive the behavior of the index at orders $\beta^{-2},\beta^{-1},\beta^0$. We also make a conjecture for $O(\beta)$, where we argue that the expansion truncates up to exponentially small corrections. An important point is the existence of vector multiplet zero modes, unaccompanied by massless matter fields. The runaway of Affleck-Harvey-Witten is however avoided by a non-perturbative confinement mechanism. This confinement mechanism guarantees that our results are robust.

  61 citations

• Quantum field theory and the Bieberbach conjecture

  Parthiv Haldar, Aninda Sinha, Ahmadullah Zahed

  SciPost Phys. 11, 002 (2021) · published 8 July 2021 | Toggle abstract · pdf

  An intriguing correspondence between ingredients in geometric function theory related to the famous Bieberbach conjecture (de Branges' theorem) and the non-perturbative crossing symmetric representation of 2-2 scattering amplitudes of identical scalars is pointed out. Using the dispersion relation and unitarity, we are able to derive several inequalities, analogous to those which arise in the discussions of the Bieberbach conjecture. We derive new and strong bounds on the ratio of certain Wilson coefficients and demonstrate that these are obeyed in one-loop $\phi^4$ theory, tree level string theory as well as in the S-matrix bootstrap. Further, we find two sided bounds on the magnitude of the scattering amplitude, which are shown to be respected in all the contexts mentioned above. Translated to the usual Mandelstam variables, for large $|s|$, fixed $t$, the upper bound reads $|\mathcal{M}(s,t)|\lesssim |s^2|$. We discuss how Szegö's theorem corresponds to a check of univalence in an EFT expansion, while how the Grunsky inequalities translate into nontrivial, nonlinear inequalities on the Wilson coefficients.

  36 citations

• Gravitational waves from an axion-dark photon system: A lattice study

  Wolfram Ratzinger, Pedro Schwaller, Ben A. Stefanek

  SciPost Phys. 11, 001 (2021) · published 6 July 2021 | Toggle abstract · pdf

  In this work, we present a lattice study of an axion - dark photon system in the early Universe and show that the stochastic gravitational wave (GW) background produced by this system may be probed by future GW experiments across a vast range of frequencies. The numerical simulation on the lattice allows us to take into account non-linear backreaction effects and enables us to accurately predict the final relic abundance of the axion or axion-like particle (ALP) as well as its inhomogeneities, and gives a more precise prediction of the GW spectrum. Importantly, we find that the GW spectrum has more power at high momenta due to $2\rightarrow1$ processes. Furthermore, we find the degree of polarization of the peak of the GW spectrum depends on the ALP-dark photon coupling and that the polarization can be washed out or even flipped for large values thereof. In line with recent results in the literature, we find the ALP relic abundance may be suppressed by two orders of magnitude and discuss possible extensions of the model that expand the viable parameter space. Finally, we discuss the possibility to probe ultralight ALP dark matter via spectral distortions of the CMB.

  23 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

• 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

• Using machine learning to disentangle LHC signatures of Dark Matter candidates

  Charanjit Kaur Khosa, Veronica Sanz, Michael Soughton

  SciPost Phys. 10, 151 (2021) · published 22 June 2021 | Toggle abstract · pdf

  We study the prospects of characterising Dark Matter at colliders using Machine Learning (ML) techniques. We focus on the monojet and missing transverse energy (MET) channel and propose a set of benchmark models for the study: a typical WIMP Dark Matter candidate in the form of a SUSY neutralino, a pseudo-Goldstone impostor in the shape of an Axion-Like Particle, and a light Dark Matter impostor whose interactions are mediated by a heavy particle. All these benchmarks are tensioned against each other, and against the main SM background ($Z$+jets). Our analysis uses both the leading-order kinematic features as well as the information of an additional hard jet. We explore different representations of the data, from a simple event data sample with values of kinematic variables fed into a Logistic Regression algorithm or a Fully Connected Neural Network, to a transformation of the data into images related to probability distributions, fed to Deep and Convolutional Neural Networks. We also study the robustness of our method against including detector effects, dropping kinematic variables, or changing the number of events per image. In the case of signals with more combinatorial possibilities (events with more than one hard jet), the most crucial data features are selected by performing a Principal Component Analysis. We compare the performance of all these methods, and find that using the 2D images of the combined information of multiple events significantly improves the discrimination performance.

  15 citations

• Topological field theory approach to intermediate statistics

  Ward L. Vleeshouwers, Vladimir Gritsev

  SciPost Phys. 10, 146 (2021) · published 16 June 2021 | Toggle abstract · pdf

  Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are characterized by the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szegö’s limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of $U(N)$ Chern-Simons theory on $S^3$ , and the SFF of this ensemble is proportional to the HOMFLY invariant of (2n,2)-torus links with one component in the fundamental and one in the antifundamental representation. This is one example of a large class of ensembles with intermediate statistics arising from topological field and string theories. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.

  7 citations

• Applications of dispersive sum rules: $ε$-expansion and holography

  Dean Carmi, Joao Penedones, Joao A. Silva, Alexander Zhiboedov

  SciPost Phys. 10, 145 (2021) · published 14 June 2021 | Toggle abstract · pdf

  We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in $d=4-\epsilon$ dimensions. We re-derive many of the known results to order $\epsilon^4$ and we make new predictions. No assumption of analyticity down to spin $0$ was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

  36 citations