Publications

Order by: publication date number of citations

• A coupling prescription for post-Newtonian corrections in quantum mechanics

  Jelle Hartong, Emil Have, Niels A. Obers, Igor Pikovski

  SciPost Phys. 16, 088 (2024) · published 27 March 2024 | Toggle abstract · pdf

  The interplay between quantum theory and general relativity remains one of the main challenges of modern physics. A renewed interest in the low-energy limit is driven by the prospect of new experiments that could probe this interface. Here we develop a covariant framework for expressing post-Newtonian corrections to Schrödinger's equation on arbitrary gravitational backgrounds based on a $1/c^2$ expansion of Lorentzian geometry, where $c$ is the speed of light. Our framework provides a generic coupling prescription of quantum systems to gravity that is valid in the intermediate regime between Newtonian gravity and General Relativity, and that retains the focus on geometry. At each order in $1/c^2$ this produces a nonrelativistic geometry to which quantum systems at that order couple. By considering the gauge symmetries of both the nonrelativistic geometries and the $1/c^2$ expansion of the complex Klein-Gordon field, we devise a prescription that allows us to derive the Schrödinger equation and its post-Newtonian corrections on a gravitational background order-by-order in $1/c^2$. We also demonstrate that these results can be obtained from a $1/c^2$ expansion of the complex Klein-Gordon Lagrangian. We illustrate our methods by performing the $1/c^2$ expansion of the Kerr metric up to $\mathcal{O}(c^{-2})$, which leads to a special case of the Hartle-Thorne metric. The associated Schrödinger equation captures novel and potentially measurable effects.

  7 citations

• Bulk locality and asymptotic causal diamonds

  Chethan Krishnan

  SciPost Phys. 7, 057 (2019) · published 29 October 2019 | Toggle abstract · pdf

  In AdS/CFT, the non-uniqueness of the reconstructed bulk from boundary subregions has motivated the notion of code subspaces. We present some closely related structures that arise in flat space. A useful organizing idea is that of an $asymptotic$ causal diamond (ACD): a causal diamond attached to the conformal boundary of Minkowski space. The space of ACDs is defined by pairs of points, one each on the future and past null boundaries, ${\cal I}^{\pm}$. We observe that for flat space with an IR cut-off, this space (a) encodes a preferred class of boundary subregions, (b) is a plausible way to capture holographic data for local bulk reconstruction, (c) has a natural interpretation as the kinematic space for holography, (d) leads to a holographic entanglement entropy in flat space that matches previous definitions and satisfies strong sub-additivity, and, (e) has a bulk union/intersection structure isomorphic to the one that motivated the introduction of quantum error correction in AdS/CFT. By sliding the cut-off, we also note one substantive way in which flat space holography differs from that in AdS. Even though our discussion is centered around flat space (and AdS), we note that there are notions of ACDs in other spacetimes as well. They could provide a covariant way to abstractly characterize tensor sub-factors of Hilbert spaces of holographic theories.

  7 citations

• Benchmarking the Ising universality class in $3 \le d < 4$ dimensions

  Claudio Bonanno, Andrea Cappelli, Mikhail Kompaniets, Satoshi Okuda, Kay Joerg Wiese

  SciPost Phys. 14, 135 (2023) · published 30 May 2023 | Toggle abstract · pdf

  The Ising critical exponents $\eta$, $\nu$ and $\omega$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.

  7 citations

• Parent Hamiltonians of Jastrow wavefunctions

  Mathieu Beau, Adolfo del Campo

  SciPost Phys. Core 4, 030 (2021) · published 18 November 2021 | Toggle abstract · pdf

  We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to arbitrary spatial dimensions. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.

  7 citations

• Marginal deformations from type IIA supergravity

  Nikolay Bobev, Pieter Bomans, Fridrik Freyr Gautason, Vincent S. Min

  SciPost Phys. 10, 140 (2021) · published 10 June 2021 | Toggle abstract · pdf

  We study marginal deformations of a class of three-dimensional $\mathcal{N}=2$ SCFTs that admit a holographic dual description in massive type IIA supergravity. We compute the dimension of the conformal manifold in these SCFTs and identify a special submanifold with enhanced flavor symmetry. We show how to apply the TsT transformation of Lunin-Maldacena to construct explicit supersymmetric AdS$_4$ solutions of massive type IIA supergravity with non-trivial internal fluxes that are the holographic dual of these marginal deformations. Finally, we also briefly comment on a class of RG flows between some of these SCFTs that also admit a holographic realization.

  7 citations

• The Conformal Spectrum of Non-Abelian Anyons

  Nima Doroud, David Tong, Carl Turner

  SciPost Phys. 4, 022 (2018) · published 30 April 2018 | Toggle abstract · pdf

  We study the spectrum of multiple non-Abelian anyons in a harmonic trap. The system is described by Chern-Simons theory, coupled to either bosonic or fermionic non-relativistic matter, and has an SO(2,1) conformal invariance. We describe a number of special properties of the spectrum, focussing on a class of protected states whose energies are dictated by their angular momentum. We show that the angular momentum of a bound state of non-Abelian anyons is determined by the quadratic Casimirs of their constituents.

  7 citations

• Quantum error correction and large $N$

  Alexey Milekhin

  SciPost Phys. 11, 094 (2021) · published 19 November 2021 | Toggle abstract · pdf

  In recent years quantum error correction (QEC) has become an important part of AdS/CFT. Unfortunately, there are no field-theoretic arguments about why QEC holds in known holographic systems. The purpose of this paper is to fill this gap by studying the error correcting properties of the fermionic sector of various large $N$ theories. Specifically we examine $SU(N)$ matrix quantum mechanics and 3-rank tensor $O(N)^3$ theories. Both of these theories contain large gauge groups. We argue that gauge singlet states indeed form a quantum error correcting code. Our considerations are based purely on large $N$ analysis and do not appeal to a particular form of Hamiltonian or holography.

  7 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

• Mirror symmetry for five-parameter Hulek-Verrill manifolds

  Philip Candelas, Xenia de la Ossa, Pyry Kuusela, Joseph McGovern

  SciPost Phys. 15, 144 (2023) · published 6 October 2023 | Toggle abstract · pdf

  We study the mirrors of five-parameter Calabi-Yau threefolds first studied by Hulek and Verrill in the context of observed modular behaviour of the zeta functions for Calabi-Yau manifolds. Toric geometry allows for a simple explicit construction of these mirrors, which turn out to be familiar manifolds. These are elliptically fibred in multiple ways. By studying the singular fibres, we are able to identify the rational curves of low degree on the mirror manifolds. This verifies the mirror symmetry prediction obtained by studying the mirror map near large complex structure points. We undertake also an extensive study of the periods of the Hulek-Verrill manifolds and their monodromies. On the mirror, we compute the genus-zero and -one instanton numbers, which are labelled by 5 indices, as $h^{1,1}\!=5$. There is an obvious permutation symmetry on these indices, but in addition there is a surprising repetition of values. We trace this back to an $S_{6}$ symmetry made manifest by certain constructions of the complex structure moduli space of the Hulek-Verrill manifold. Among other consequences, we see in this way that the moduli space has six large complex structure limits. It is the freedom to expand the prepotential about any one of these points that leads to this symmetry in the instanton numbers. An intriguing fact is that the group that acts on the instanton numbers is larger than $S_6$ and is in fact an infinite hyperbolic Coxeter group, that we study. The group orbits have a "web" structure, and with certain qualifications the instanton numbers are only nonzero if they belong to what we term "positive webs". This structure has consequences for instanton numbers at all genera.

  7 citations

• Deconstructing little strings with $\mathcal{N}=1$ gauge theories on ellipsoids

  Joseph Hayling, Rodolfo Panerai, Constantinos Papageorgakis

  SciPost Phys. 4, 042 (2018) · published 28 June 2018 | Toggle abstract · pdf

  A formula was recently proposed for the perturbative partition function of certain $\mathcal N=1$ gauge theories on the round four-sphere, using an analytic-continuation argument in the number of dimensions. These partition functions are not currently accessible via the usual supersymmetric-localisation technique. We provide a natural refinement of this result to the case of the ellipsoid. We then use it to write down the perturbative partition function of an $\mathcal N=1$ toroidal-quiver theory (a double orbifold of $\mathcal N=4$ super Yang-Mills) and show that, in the deconstruction limit, it reproduces the zero-winding contributions to the BPS partition function of (1,1) Little String Theory wrapping an emergent torus. We therefore successfully test both the expressions for the $\mathcal N=1$ partition functions, as well as the relationship between the toroidal-quiver theory and Little String Theory through dimensional deconstruction.

  7 citations