Publications

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• Conformal bootstrap bounds for the $U(1)$ Dirac spin liquid and $N=7$ Stiefel liquid

  Yin-Chen He, Junchen Rong, Ning Su

  SciPost Phys. 13, 014 (2022) · published 8 August 2022 | Toggle abstract · pdf

  We apply the conformal bootstrap technique to study the $U(1)$ Dirac spin liquid (i.e. $N_f=4$ QED$_3$) and the newly proposed $N=7$ Stiefel liquid (i.e. a conjectured 3d non-Lagrangian CFT without supersymmetry). For the $N_f=4$ QED$_3$, we focus on the monopole operator and ($SU(4)$ adjoint) fermion bilinear operator. We bootstrap their single correlators as well as the mixed correlators between them. We first discuss the bootstrap kinks from single correlators. Some exponents of these bootstrap kinks are close to the expected values of QED$_3$, but we provide clear evidence that they should not be identified as the QED$_3$. By requiring the critical phase to be stable on the triangular and the kagome lattice, we obtain rigorous numerical bounds for the $U(1)$ Dirac spin liquid and the Stiefel liquid. For the triangular and kagome Dirac spin liquid, the rigorous lower bounds of the monopole operator's scaling dimension are $1.046$ and $1.105$, respectively. These bounds are consistent with the latest Monte Carlo results.

  16 citations

• Multiple relaxation times in perturbed XXZ chain

  M. Mierzejewski, J. Pawłowski, P. Prelovšek, J. Herbrych

  SciPost Phys. 13, 013 (2022) · published 5 August 2022 | Toggle abstract · pdf

  We study numerically the relaxation of correlation functions in weakly perturbed integrable XXZ chain. While the decay of spin-current and energy-current correlations at zero magnetization are well described by single, but quite distinct, relaxation rates governed by the square of the perturbation strength $g$, the correlations at finite magnetization reveal multiple relaxation rates. The result can be understood in terms of decays of several quantities, conserved in the reference integrable system. On the other hand, the correlations of non-commuting quantities, being conserved at particular anisotropies $\Delta$, decay non-exponentially with characteristic time scale linear in $g$.

  5 citations

• On Current-Squared Flows and ModMax Theories

  Christian Ferko, Liam Smith, Gabriele Tartaglino-Mazzucchelli

  SciPost Phys. 13, 012 (2022) · published 4 August 2022 | Toggle abstract · pdf

  We show that the recently introduced ModMax theory of electrodynamics and its Born-Infeld-like generalization are related by a flow equation driven by a quadratic combination of stress-energy tensors. The operator associated to this flow is a $4d$ analogue of the $T\bar{T}$ deformation in two dimensions. This result generalizes the observation that the ordinary Born-Infeld Lagrangian is related to the free Maxwell theory by a current-squared flow. As in that case, we show that no analogous relationship holds in any other dimension besides $d=4$. We also demonstrate that the $\mathcal{N}=1$ supersymmetric version of the ModMax-Born-Infeld theory obeys a related supercurrent-squared flow which is formulated directly in $\mathcal{N}=1$ superspace.

  32 citations

• Hamiltonian Truncation Effective Theory

  Timothy Cohen, Kara Farnsworth, Rachel Houtz, Markus A. Luty

  SciPost Phys. 13, 011 (2022) · published 4 August 2022 | Toggle abstract · pdf

  Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian $H_0$ with eigenvalues below some energy cutoff $E_\text{max}$. In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above $E_\text{max}$. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of $1/E_\text{max}$. The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of $H_0/E_\text{max}$. The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D $\lambda \phi^4$ theory, and compute the the leading $1/E_\text{max}^2$ corrections to the effective Hamiltonian. We show that these corrections non-trivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order $1/E_\text{max}^3$, as expected by our power counting. We also present the power counting for 3D $\lambda \phi^4$ theory and perform calculations that demonstrate the separation of scales in this theory.

  4 citations

• Scattering and Strebel graphs

  Pronobesh Maity

  SciPost Phys. 13, 010 (2022) · published 26 July 2022 | Toggle abstract · pdf

  We consider a special scattering experiment with n particles in $\mathbb{R}^{n-3,1}$. The scattering equations in this set-up become the saddle-point equations of a Penner-like matrix model, where in the large $n$ limit, the spectral curve is directly related to the unique Strebel differential on a Riemann sphere with three punctures. The solutions to the scattering equations localize along different kinds of graphs, tuned by a kinematic variable. We conclude with a few comments on a connection between these graphs and scattering in the Gross-Mende limit.

  1 citation

• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation

  Miguel Alvarado, Alfredo Levy Yeyati

  SciPost Phys. 13, 009 (2022) · published 25 July 2022 | Toggle abstract · pdf

  Since the breakthrough of twistronics a plethora of topological phenomena in correlated systems has appeared. These devices can be typically analyzed in terms of lattice models using Green's function techniques. In this work we introduce a general method to obtain the boundary Green's function of such models taking advantage of the numerical Faddeev-LeVerrier algorithm to circumvent some analytical constraints of previous works. We illustrate our formalism analyzing the edge features of a Chern insulator, the Kitaev square lattice model for a topological superconductor and the Checkerboard lattice hosting topological flat bands. The efficiency and accuracy of the method is demonstrated by comparison to standard recursive Green's function calculations and direct diagonalizations.

  3 citations

• Scattering Amplitudes and BCFW in $\mathcal{N}=2^*$ Theory

  Md. Abhishek, Subramanya Hegde, Dileep P. Jatkar, Arnab Priya Saha

  SciPost Phys. 13, 008 (2022) · published 25 July 2022 | Toggle abstract · pdf

  We use massive spinor helicity formalism to study scattering amplitudes in $\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute amplitudes using projection from $\mathcal{N}=4$ theory and write three point amplitudes in a convenient form using special kinematics. We then compute four point amplitudes by carrying out massive BCFW shifts of the amplitudes. We find some of the shifted amplitudes have a pole at $z=\infty$. Taking the residue at $z=\infty$ into account ensures little group covariance of the final result.

  5 citations

• Benchmarking LHC searches for light 2HDM+a pseudoscalars

  Spyros Argyropoulos, Ulrich Haisch

  SciPost Phys. 13, 007 (2022) · published 22 July 2022 | Toggle abstract · pdf

  Using two suitable benchmark scenarios that satisfy the experimental con- straints on the total decay width of the 125 GeV Higgs boson, we determine the bounds on light CP-odd spin-0 states in the 2HDM+a model that arise from existing LHC searches. Our work should prove useful for 2HDM+a interpretations of future ATLAS, CMS and LHCb searches for pseudoscalars with masses below the electroweak scale.

  8 citations

• Low temperature quantum bounds on simple models

  Silvia Pappalardi, Jorge Kurchan

  SciPost Phys. 13, 006 (2022) · published 22 July 2022 | Toggle abstract · pdf

  In the past few years, there has been considerable activity around a set of quantum bounds on transport coefficients (viscosity) and chaos (Lyapunov exponent), relevant at low temperatures. The interest comes from the fact that Black-Hole models seem to saturate all of them. The goal of this work is to gain physical intuition about the quantum mechanisms that enforce these bounds on simple models. To this aim, we consider classical and quantum free dynamics on curved manifolds. These systems exhibit chaos up to the lowest temperatures and - as we discuss - they violate the bounds in the classical limit. First of all, we show that the quantum dimensionless viscosity and the Lyapunov exponent only depend on the de Broglie length and a geometric length-scale, thus establishing the scale at which quantum effects become relevant. Then, we focus on the bound on the Lyapunov exponent and identify three different ways in which quantum effects arise in practice. We illustrate our findings on a toy model given by the surface of constant negative curvature - a paradigmatic model of quantum chaos - glued to a cylinder. By exact solution and numerical investigations, we show how the chaotic behaviour is limited by the quantum effects of the curvature itself. Interestingly, we find that at the lowest energies the bound to chaos is dominated by the longest length scales, and it is therefore a collective effect.

  7 citations

• 3d $\mathcal{N}=4$ Gauge Theories on an Elliptic Curve

  Mathew Bullimore, Daniel Zhang

  SciPost Phys. 13, 005 (2022) · published 22 July 2022 | Toggle abstract · pdf

  This paper studies $3d$ $\mathcal{N}=4$ supersymmetric gauge theories on an elliptic curve, with the aim to provide a physical realisation of recent constructions in equivariant elliptic cohomology of symplectic resolutions. We first study the Berry connection for supersymmetric ground states in the presence of mass parameters and flat connections for flavour symmetries, which results in a natural construction of the equivariant elliptic cohomology variety of the Higgs branch. We then investigate supersymmetric boundary conditions and show from an analysis of boundary 't Hooft anomalies that their boundary amplitudes represent equivariant elliptic cohomology classes. We analyse two distinguished classes of boundary conditions known as exceptional Dirichlet and enriched Neumann, which are exchanged under mirror symmetry. We show that the boundary amplitudes of the latter reproduce elliptic stable envelopes introduced by Aganagic-Okounkov, and relate boundary amplitudes of the mirror symmetry interface to the mother function in equivariant elliptic cohomology. Finally, we consider correlation functions of Janus interfaces for varying mass parameters, recovering the chamber R-matrices of elliptic integrable systems.

  9 citations