Publications

Order by: publication date number of citations

• The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking

  Álvaro Pastor-Gutiérrez, Jan M. Pawlowski, Manuel Reichert

  SciPost Phys. 15, 105 (2023) · published 20 September 2023 | Toggle abstract · pdf

  We present a comprehensive non-perturbative study of the phase structure of the asymptotically safe Standard Model. The physics scales included range from the asymptotically safe trans-Planckian regime in the ultraviolet, the intermediate high-energy regime with electroweak symmetry breaking to strongly correlated QCD in the infrared. All flows are computed with a self-consistent functional renormalisation group approach, using a vertex expansion in the fluctuation fields. In particular, this approach takes care of all physical threshold effects and the respective decoupling of ultraviolet degrees of freedom. Standard Model and gravity couplings and masses are fixed by their experimental low energy values. Importantly, we accommodate for the difference between the top pole mass and its Euclidean analogue. Both, the correct mass determination and the threshold effects have a significant impact on the qualitative properties, and in particular on the stability properties of the specific ultraviolet-infrared trajectory with experimental Standard Model physics in the infrared. We show that in the present rather advanced approximation the matter part of the asymptotically safe Standard Model has the same number of relevant parameters as the Standard Model, and is asymptotically free. This result is based on the novel UV fixed point found in the present work: the fixed point Higgs potential is flat but has two relevant directions. These results and their analysis are accompanied by a thorough discussion of the systematic error of the present truncation, also important for systematic improvements.

  7 citations

• Looking for structure in the cobordism conjecture

  David Andriot, Nils Carqueville, Niccolò Cribiori

  SciPost Phys. 13, 071 (2022) · published 28 September 2022 | Toggle abstract · pdf

  The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead tower construction as a possible organising principle for the topological structures entering the formulation of the conjecture. We discuss why and how to include geometric structures in bordism groups, such as higher U(1)-bundles with connection. The inclusion of magnetic defects is also addressed in some detail. We further elaborate on how the conjecture could predict Kaluza--Klein monopoles, and we study the gravity decoupling limit in the cobordism conjecture, with a few observations on NSNS string backgrounds. We end with comments in relation to T-duality, as well as the finiteness conjecture.

  7 citations

• Tripartite information at long distances

  César A. Agón, Pablo Bueno, Horacio Casini

  SciPost Phys. 12, 153 (2022) · published 10 May 2022 | Toggle abstract · pdf

  We compute the leading term of the tripartite information at long distances for three spheres in a CFT. This falls as $r^{-6\Delta}$, where $r$ is the typical distance between the spheres, and $\Delta$, the lowest primary field dimension. The coefficient turns out to be a combination of terms coming from the two- and three-point functions and depends on the OPE coefficient of the field. We check the result with three-dimensional free scalars in the lattice finding excellent agreement. When the lowest-dimensional field is a scalar, we find that the mutual information can be monogamous only for quite large OPE coefficients, far away from a perturbative regime. When the lowest-dimensional primary is a fermion, we argue that the scaling must always be faster than $r^{-6\Delta_f}$. In particular, lattice calculations suggest a leading scaling $ r^{-(6\Delta_f+1)}$. For free fermions in three dimensions, we show that mutual information is also non-monogamous in the long-distance regime.

  7 citations

• The edge of chaos: quantum field theory and deep neural networks

  Kevin T. Grosvenor, Ro Jefferson

  SciPost Phys. 12, 081 (2022) · published 3 March 2022 | Toggle abstract · pdf

  We explicitly construct the quantum field theory corresponding to a general class of deep neural networks encompassing both recurrent and feedforward architectures. We first consider the mean-field theory (MFT) obtained as the leading saddlepoint in the action, and derive the condition for criticality via the largest Lyapunov exponent. We then compute the loop corrections to the correlation function in a perturbative expansion in the ratio of depth T to width N, and find a precise analogy with the well-studied O(N) vector model, in which the variance of the weight initializations plays the role of the 't Hooft coupling. In particular, we compute both the O(1) corrections quantifying fluctuations from typicality in the ensemble of networks, and the subleading O(T/N) corrections due to finite-width effects. These provide corrections to the correlation length that controls the depth to which information can propagate through the network, and thereby sets the scale at which such networks are trainable by gradient descent. Our analysis provides a first-principles approach to the rapidly emerging NN-QFT correspondence, and opens several interesting avenues to the study of criticality in deep neural networks.

  7 citations

• Finite-size corrections for universal boundary entropy in bond percolation

  Jan de Gier, Jesper Lykke Jacobsen, Anita Ponsaing

  SciPost Phys. 1, 012 (2016) · published 19 December 2016 | Toggle abstract · pdf

  We compute the boundary entropy for bond percolation on the square lattice in the presence of a boundary loop weight, and prove explicit and exact expressions on a strip and on a cylinder of size $L$. For the cylinder we provide a rigorous asymptotic analysis which allows for the computation of finite-size corrections to arbitrary order. For the strip we provide exact expressions that have been verified using high-precision numerical analysis. Our rigorous and exact results corroborate an argument based on conformal field theory, in particular concerning universal logarithmic corrections for the case of the strip due to the presence of corners in the geometry. We furthermore observe a crossover at a special value of the boundary loop weight.

  7 citations

• Out of time ordered effective dynamics of a quartic oscillator

  Bidisha Chakrabarty, Soumyadeep Chaudhuri

  SciPost Phys. 7, 013 (2019) · published 29 July 2019 | Toggle abstract · pdf

  We study the dynamics of a quantum Brownian particle weakly coupled to a thermal bath. Working in the Schwinger-Keldysh formalism, we develop an effective action of the particle up to quartic terms. We demonstrate that this quartic effective theory is dual to a stochastic dynamics governed by a non-linear Langevin equation. The Schwinger-Keldysh effective theory, or the equivalent non-linear Langevin dynamics, is insufficient to determine the out of time order correlators (OTOCs) of the particle. To overcome this limitation, we construct an extended effective action in a generalised Schwinger-Keldysh framework. We determine the additional quartic couplings in this OTO effective action and show their dependence on the bath's 4-point OTOCs. We analyse the constraints imposed on the OTO effective theory by microscopic reversibility and thermality of the bath. We show that these constraints lead to a generalised fluctuation-dissipation relation between the non-Gaussianity in the distribution of the thermal noise experienced by the particle and the thermal jitter in its damping coefficient. The quartic effective theory developed in this work provides extension of several results previously obtained for the cubic OTO dynamics of a Brownian particle.

  7 citations

• Towards quantifying information flows: relative entropy in deep neural networks and the renormalization group

  Johanna Erdmenger, Kevin T. Grosvenor, Ro Jefferson

  SciPost Phys. 12, 041 (2022) · published 26 January 2022 | Toggle abstract · pdf

  We investigate the analogy between the renormalization group (RG) and deep neural networks, wherein subsequent layers of neurons are analogous to successive steps along the RG. In particular, we quantify the flow of information by explicitly computing the relative entropy or Kullback-Leibler divergence in both the one- and two-dimensional Ising models under decimation RG, as well as in a feedforward neural network as a function of depth. We observe qualitatively identical behavior characterized by the monotonic increase to a parameter-dependent asymptotic value. On the quantum field theory side, the monotonic increase confirms the connection between the relative entropy and the c-theorem. For the neural networks, the asymptotic behavior may have implications for various information maximization methods in machine learning, as well as for disentangling compactness and generalizability. Furthermore, while both the two-dimensional Ising model and the random neural networks we consider exhibit non-trivial critical points, the relative entropy appears insensitive to the phase structure of either system. In this sense, more refined probes are required in order to fully elucidate the flow of information in these models.

  7 citations

• Many-body chaos near a thermal phase transition

  Alexander Schuckert, Michael Knap

  SciPost Phys. 7, 022 (2019) · published 19 August 2019 | Toggle abstract · pdf

  We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.

  7 citations

• Rational $Q$-systems, Higgsing and mirror symmetry

  Jie Gu, Yunfeng Jiang, Marcus Sperling

  SciPost Phys. 14, 034 (2023) · published 15 March 2023 | Toggle abstract · pdf

  The rational $Q$-system is an efficient method to solve Bethe ansatz equations for quantum integrable spin chains. We construct the rational $Q$-systems for generic Bethe ansatz equations described by an $A_{\ell-1}$ quiver, which include models with multiple momentum carrying nodes, generic inhomogeneities, generic diagonal twists and $q$-deformation. The rational $Q$-system thus constructed is specified by two partitions. Under Bethe/Gauge correspondence, the rational $Q$-system is in a one-to-one correspondence with a 3d $\mathcal{N}=4$ quiver gauge theory of the type ${T}_{{\rho}}^{{\sigma}}[\mathrm{SU}(n)]$, which is also specified by the same partitions. This shows that the rational $Q$-system is a natural language for the Bethe/Gauge correspondence, because known features of the ${T}_{{\rho}}^{{\sigma}}[\mathrm{SU}(n)]$ theories readily translate. For instance, we show that the Higgs and Coulomb branch Higgsing correspond to modifying one of the partitions in the rational $Q$-system while keeping the other untouched. Similarly, mirror symmetry is realized in terms of the rational $Q$-system by simply swapping the two partitions - exactly as for ${T}_{{\rho}}^{{\sigma}}[\mathrm{SU}(n)]$. We exemplify the computational efficiency of the rational $Q$-system by evaluating topologically twisted indices for 3d $\mathcal{N}=4$ $\mathrm{U}(n)$ SQCD theories with $n=1,\ldots,5$.

  7 citations

• Lectures on faster-than-light travel and time travel

  Barak Shoshany

  SciPost Phys. Lect. Notes 10 (2019) · published 1 October 2019 | Toggle abstract · pdf

  These lecture notes were prepared for a 25-hour course for advanced undergraduate students participating in Perimeter Institute's Undergraduate Summer Program. The lectures cover some of what is currently known about the possibility of superluminal travel and time travel within the context of established science, that is, general relativity and quantum field theory. Previous knowledge of general relativity at the level of a standard undergraduate-level introductory course is recommended, but all the relevant material is included for completion and reference. No previous knowledge of quantum field theory, or anything else beyond the standard undergraduate curriculum, is required. Advanced topics in relativity, such as causal structures, the Raychaudhuri equation, and the energy conditions are presented in detail. Once the required background is covered, concepts related to faster-than-light travel and time travel are discussed. After introducing tachyons in special relativity as a warm-up, exotic spacetime geometries in general relativity such as warp drives and wormholes are discussed and analyzed, including their limitations. Time travel paradoxes are also discussed in detail, including some of their proposed resolutions.

  7 citations