Publications

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Chaotic correlation functions with complex fermions

Ritabrata Bhattacharya, Dileep P. Jatkar, Arnab Kundu

SciPost Phys. Core 4, 018 (2021) · published 9 June 2021 | · pdf

We study correlation functions in the complex fermion SYK model. We focus, specifically, on the h = 2 mode which explicitly breaks conformal invariance and exhibits the chaotic behaviour. We explicitly compute fermion six-point function and extract the corresponding six-point OTOC which exhibits an exponential growth with maximal chaos. Following the program of Gross-Rosenhaus, this correlator contains information of the bulk cubic coupling, at the conformal point as well as perturbatively away from it. Unlike the conformal modes with high values of h, the h = 2 mode has contact interaction dominating over the planar in the large q limit.

2 citations
Stability and asymptotic interactions of chiral magnetic skyrmions in a tilted magnetic field

Bruno Barton-Singer, Bernd J. Schroers

SciPost Phys. 15, 011 (2023) · published 17 July 2023 | · pdf

Using a general framework, interaction potentials between chiral magnetic solitons in a planar system with a tilted external magnetic field are calculated analytically in the limit of large separation. The results are compared to previous numerical results for solitons with topological charge $\pm 1$. A key feature of the calculation is the interpretation of Dzyaloshinskii-Moriya interaction (DMI) as a background $SO(3)$ gauge field. In a tilted field, this leads to a $U(1)$-gauged version of the usual equation for spin excitations, leading to a distinctive oscillating interaction profile. We also obtain predictions for skyrmion stability in a tilted field which closely match numerical observations.

2 citations
Functional flows for complex effective actions

Friederike Ihssen, Jan M. Pawlowski

SciPost Phys. 15, 074 (2023) · published 31 August 2023 | · pdf

In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action. In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in $\phi^4$-theories from zero up to four dimensions. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD.

2 citations
Interface junctions in QCD${}_4$

Pranay Gorantla, Ho Tat Lam

SciPost Phys. 10, 085 (2021) · published 22 April 2021 | · pdf

We study 3+1 dimensional $SU(N)$ Quantum Chromodynamics (QCD) with $N_f$ degenerate quarks that have a spatially varying complex mass. It leads to a network of interfaces connected by interface junctions. We use anomaly inflow to constrain these defects. Based on the chiral Lagrangian and the conjectures on the interfaces, characterized by a spatially varying $\theta$-parameter, we propose a low-energy description of such networks of interfaces. Interestingly, we observe that the operators in the effective field theories on the junctions can carry baryon charges, and their spin and isospin representations coincide with baryons. We also study defects, characterized by spatially varying coupling constants, in 2+1 dimensional Chern-Simons-matter theories and in a 3+1 dimensional real scalar theory.

2 citations
The Return of the Singularities: Applications of the Smeared Null Energy Condition

Ben Freivogel, Eleni-Alexandra Kontou, Dimitrios Krommydas

SciPost Phys. 13, 001 (2022) · published 15 July 2022 | · pdf

The classic singularity theorems of General Relativity rely on energy conditions that can be violated in semiclassical gravity. Here, we provide motivation for an energy condition obeyed by semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. We then prove a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity. We also apply our bound to evaporating black holes and the traversable wormhole of Maldacena-Milekhin-Popov, and comment on the relationship of our results to other proposed semiclassical singularity theorems.

2 citations
Semi-local Bounds on Null Energy in QFT

Jackson R. Fliss, Ben Freivogel

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

2 citations
Two-parton scattering in the high-energy limit: climbing two- and three-Reggeon ladders

G. Falcioni, E. Gardi, N. Maher, C. Milloy, L. Vernazza

SciPost Phys. Proc. 7, 007 (2022) · published 20 June 2022 | · pdf

We review recent progress on the calculation of scattering amplitudes in the high-energy limit. We start by illustrating the shockwave formalism, which allows one to calculate amplitudes as iterated solutions of rapidity evolution equations. We then focus on our recent results regarding 2 -> 2 parton scattering. We present the calculation of the imaginary part of the amplitude, at next-to-leading logarithmic accuracy in the high-energy logarithms, formally to all orders, and in practice to 13 loops. We then discuss the computation of the real part of the amplitude at next-to-next-to-leading logarithmic accuracy and through four loops. Both computations are carried in full colour, and provide new insight into the analytic structure of scattering amplitudes and their infrared singularity structure.

2 citations
A plane defect in the 3d O(N) model

Abijith Krishnan, Max A. Metlitski

SciPost Phys. 15, 090 (2023) · published 12 September 2023 | · pdf

It was recently found that the classical 3d O$(N)$ model in the semi-infinite geometry can exhibit an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary falls off as $\langle \vec{S}(x) \cdot \vec{S}(0)\rangle \sim \frac{1}{(\log x)^q}$. This universality class exists for a range $2 ≤ N < N_c$ {and Monte-Carlo simulations and conformal bootstrap} indicate $N_c > 3$. In this work, we extend this {result} to the 3d O$(N)$ model in an infinite geometry with a plane defect. We use renormalization group (RG) to show that in this case the extraordinary-log universality class is present for any finite $N ≥ 2$. We additionally show, {in agreement with our RG analysis}, that the line of defect fixed points which is present at $N = ∞$ is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by $1/N$ corrections. We study the "central charge" $a$ for the $O(N)$ model in the boundary and interface geometries and provide a non-trivial detailed check of an $a$-theorem by Jensen and O'Bannon. Finally, we revisit the problem of the O$(N)$ model in the semi-infinite geometry. We find evidence that at $N = N_c$ the extraordinary and special fixed points annihilate and only the ordinary fixed point is left for $N > N_c$.

2 citations
Resurgence and renormalons in the one-dimensional Hubbard model

Marcos Mariño, Tomás Reis

SciPost Phys. 13, 113 (2022) · published 22 November 2022 | · pdf

We use resurgent analysis to study non-perturbative aspects of the one-dimensional, multicomponent Hubbard model with an attractive interaction and arbitrary filling. In the two-component case, we show that the leading Borel singularity of the perturbative series for the ground-state energy is determined by the energy gap, as expected for superconducting systems. This singularity turns out to be of the renormalon type, and we identify a class of diagrams leading to the correct factorial growth. As a consequence of our analysis, we propose an explicit expression for the energy gap at weak coupling in the multi-component Hubbard model, at next-to-leading order in the coupling constant. In the two-component, half-filled case, we use the Bethe ansatz solution to determine the full trans-series for the ground state energy, and the exact form of its Stokes discontinuity.

2 citations
Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields

Zhihan Zheng, Pei Sun, Xiaotian Xu, Tao Yang, Junpeng Cao, Wen-Li Yang

SciPost Phys. 12, 071 (2022) · published 22 February 2022 | · pdf

The thermodynamic limit and boundary energy of the isotropic spin-1 Heisenberg chain with non-diagonal boundary fields are studied. The finite size scaling properties of the inhomogeneous term in the $T-Q$ relation at the ground state are calculated by the density matrix renormalization group. Based on our findings, the boundary energy of the system in the thermodynamic limit can be obtained from Bethe ansatz equations of a related model with parallel boundary fields. These results can be generalized to the $SU(2)$ symmetric high spin Heisenberg model directly.

2 citations

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