Publications

Order by: publication date number of citations

• Exceptional Chern-Simons-Matter dualities

  Clay Córdova, Po-Shen Hsin, Kantaro Ohmori

  SciPost Phys. 7, 056 (2019) · published 28 October 2019 | Toggle abstract · pdf

  We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is $(E_{N})_{1}\leftrightarrow SU(9-N)_{-1}$. Others such as $SO(3)_{8}\leftrightarrow PSU(3)_{-6},$ are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant $G_{2}$ gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

  22 citations

• Physical representations for scattering amplitudes and the wavefunction of the universe

  Paolo Benincasa, William J. Torres Bobadilla

  SciPost Phys. 12, 192 (2022) · published 10 June 2022 | Toggle abstract · pdf

  The way we organise perturbation theory is of fundamental importance both for computing the observables of relevance and for extracting fundamental physics out of them. If on one hand the different ways in which the perturbative observables can be written make manifest different features ({\it e.g.} symmetries as well as principles such as unitarity, causality and locality), on the other hand precisely demanding that some concrete features are manifest lead to different ways of organising perturbation theory. In the context of flat-space scattering amplitudes, a number of them are already known and exploited, while much less is known for cosmological observables. In the present work, we show how to systematically write down both the wavefunction of the universe and the flat-space scattering amplitudes, in such a way that they manifestly show physical poles only. We make use of the invariant definition of such observables in terms of {\it cosmological polytopes} and their {\it scattering facet}. In particular, we show that such representations correspond to triangulations of such objects through hyperplanes identified by the intersection of their facets outside of them. All possible triangulations of this type generate the different representations. This allows us to provide a general proof for the conjectured all-loop causal representation of scattering amplitudes. Importantly, all such representations can be viewed as making explicit a subset of compatible singularities, and our construction provides a way to extend Steinmann relations to higher codimension singularities for both the flat-space scattering amplitudes and the cosmological wavefunction.

  22 citations

• Exactly solvable lattice Hamiltonians and gravitational anomalies

  Yu-An Chen, Po-Shen Hsin

  SciPost Phys. 14, 089 (2023) · published 2 May 2023 | Toggle abstract · pdf

  We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary $\mathbb{Z}_2$ topological order with fermionic particle and fermionic loop excitations that have mutual $\pi$ statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary $\mathbb{Z}_2$ symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.

  22 citations

• Exotic invertible phases with higher-group symmetries

  Po-Shen Hsin, Wenjie Ji, Chao-Ming Jian

  SciPost Phys. 12, 052 (2022) · published 3 February 2022 | Toggle abstract · pdf

  We investigate a family of invertible phases of matter with higher-dimensional exotic excitations in even spacetime dimensions, which includes and generalizes the Kitaev's chain in 1+1d. The excitation has $\mathbb{Z}_2$ higher-form symmetry that mixes with the spacetime Lorentz symmetry to form a higher group spacetime symmetry. We focus on the invertible exotic loop topological phase in 3+1d. This invertible phase is protected by the $\mathbb{Z}_2$ one-form symmetry and the time-reversal symmetry, and has surface thermal Hall conductance not realized in conventional time-reversal symmetric ordinary bosonic systems without local fermion particles and the exotic loops. We describe a UV realization of the invertible exotic loop topological order using the $SO(3)_-$ gauge theory with unit discrete theta parameter, which enjoys the same spacetime two-group symmetry. We discuss several applications including the analogue of ``fermionization'' for ordinary bosonic theories with $\mathbb{Z}_2$ non-anomalous internal higher-form symmetry and time-reversal symmetry.

  22 citations

• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections

  Salvatore D. Pace, Guilherme Delfino, Ho Tat Lam, Ömer M. Aksoy

  SciPost Phys. 18, 021 (2025) · published 17 January 2025 | Toggle abstract · pdf

  Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in ${1+1}$ dimensions. Working with local Hamiltonians of spin chains, we explore the dual symmetries after gauging and their potential new spatial modulations. We establish sufficient conditions for the existence of an isomorphism between the modulated symmetries and their dual, naturally implemented by lattice reflections. For instance, in systems of prime qudits, translation invariance guarantees this isomorphism. For non-prime qudits, we show using techniques from ring theory that this isomorphism can also exist, although it is not guaranteed by lattice translation symmetry alone. From this isomorphism, we identify new Kramers-Wannier dualities and construct related non-invertible reflection symmetry operators using sequential quantum circuits. Notably, this non-invertible reflection symmetry exists even when the system lacks ordinary reflection symmetry. Throughout the paper, we illustrate these results using various simple toy models.

  22 citations

• Field Theory of Interacting Boundary Gravitons

  Stephen Ebert, Eliot Hijano, Per Kraus, Ruben Monten, Richard M. Myers

  SciPost Phys. 13, 038 (2022) · published 29 August 2022 | Toggle abstract · pdf

  Pure three-dimensional gravity is a renormalizable theory with two free parameters labelled by $G$ and $\Lambda$. As a consequence, correlation functions of the boundary stress tensor in AdS$_3$ are uniquely fixed in terms of one dimensionless parameter, which is the central charge of the Virasoro algebra. The same argument implies that AdS$_3$ gravity at a finite radial cutoff is a renormalizable theory, but now with one additional parameter corresponding to the cutoff location. This theory is conjecturally dual to a $T\overline{T}$-deformed CFT, assuming that such theories actually exist. To elucidate this, we study the quantum theory of boundary gravitons living on a cutoff planar boundary and the associated correlation functions of the boundary stress tensor. We compute stress tensor correlation functions to two-loop order ($G$ being the loop counting parameter), extending existing tree level results. This is made feasible by the fact that the boundary graviton action simplifies greatly upon making a judicious field redefinition, turning into the Nambu-Goto action. After imposing Lorentz invariance, the correlators at this order are found to be unambiguous up to a single undetermined renormalization parameter.

  22 citations

• Bounds on quantum evolution complexity via lattice cryptography

  Ben Craps, Marine De Clerck, Oleg Evnin, Philip Hacker, Maxim Pavlov

  SciPost Phys. 13, 090 (2022) · published 11 October 2022 | Toggle abstract · pdf

  We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-dependent evolution operator and the origin within the group of unitaries. (An appropriate 'complexity metric' must be used that takes into account the relative difficulty of performing 'nonlocal' operations that act on many degrees of freedom at once.) While simply formulated and geometrically attractive, this notion of complexity is numerically intractable save for toy models with Hilbert spaces of very low dimensions. To bypass this difficulty, we trade the exact definition in terms of geodesics for an upper bound on complexity, obtained by minimizing the distance over an explicitly prescribed infinite set of curves, rather than over all possible curves. Identifying this upper bound turns out equivalent to the closest vector problem (CVP) previously studied in integer optimization theory, in particular, in relation to lattice-based cryptography. Effective approximate algorithms are hence provided by the existing mathematical considerations, and they can be utilized in our analysis of the upper bounds on quantum evolution complexity. The resulting algorithmically implemented complexity bound systematically assigns lower values to integrable than to chaotic systems, as we demonstrate by explicit numerical work for Hilbert spaces of dimensions up to $\sim 10^4$.

  22 citations

• Effective fractonic behavior in a two-dimensional exactly solvable spin liquid

  Guilherme Delfino, Weslei Bernardino Fontana, Pedro R. S. Gomes, Claudio Chamon

  SciPost Phys. 14, 002 (2023) · published 12 January 2023 | Toggle abstract · pdf

  In this work we propose a $\mathbb{Z}_N$ clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility, that resemble fractonic physics from higher dimensional models. We then study the continuum descriptions for the lattice system in two distinct regimes and find two qualitative distinct field theories for each one of them. A characteristic time scale that grows exponentially fast with $N^2$ (and diverges rapidly as function of system parameters) separates these two regimes. For times below this scale, the system is described by an effective fractonic Chern-Simons-like action, where higher-form symmetries prevent quasiparticles from hopping. In this regime, the system behaves effectively as a fracton as isolated particles, in practice, never leave their original position. Beyond the large characteristic time scale, the excitations are mobile and the effective field theory is given by a pure mutual Chern-Simons action. In this regime, the UV/IR properties of the system is captured by a peculiar realization of the translation group.

  22 citations

• Bubble instabilities of mIIA on AdS$_4\times S^6$

  Pieter Bomans, Davide Cassani, Giuseppe Dibitetto, Nicolò Petri

  SciPost Phys. 12, 099 (2022) · published 18 March 2022 | Toggle abstract · pdf

  We consider compactifications of massive IIA supergravity on a six-sphere. This setup is known to give rise to non-supersymmetric AdS$_4$ vacua preserving SO$(7)$ as well as G$_2$ residual symmetry. Both solutions have a round $S^6$ metric and are supported by the Romans’ mass and internal $F_6$ flux. While the SO$(7)$ invariant vacuum is known to be perturbatively unstable, the G$_2$ invariant one has been found to have a fully stable Kaluza-Klein spectrum. Moreover, it has been shown to be protected against brane-jet instabilities. Motivated by these results, we study possible bubbling solutions connected to the G$_2$ vacuum, representing non-perturbative instabilities of the latter. We indeed find an instability channel represented by the nucleation of a bubble of nothing dressed up with a homogeneous D2 brane charge distribution in the internal space. Our solution generalizes to the case where $S^6$ is replaced by any six-dimensional nearly-Kähler manifold.

  21 citations

• The quasilocal degrees of freedom of Yang-Mills theory

  Henrique Gomes, Aldo Riello

  SciPost Phys. 10, 130 (2021) · published 4 June 2021 | Toggle abstract · pdf

  Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. We employ geometric methods rooted in the functional geometry of the phase space of Yang-Mills theories to: (\textit{1}) characterize a basis for quasilocal degrees of freedom (dof) that is manifestly gauge-covariant also at the boundary; (\textit{2}) tame the non-additivity of the regional symplectic forms upon the gluing of regions; and to (\textit{3}) discuss gauge and global charges in both Abelian and non-Abelian theories from a geometric perspective. Naturally, our analysis leads to splitting the Yang-Mills dof into Coulombic and radiative. Coulombic dof enter the Gauss constraint and are dependent on extra boundary data (the electric flux); radiative dof are unconstrained and independent. The inevitable non-locality of this split is identified as the source of the symplectic non-additivity, i.e. of the appearance of new dof upon the gluing of regions. Remarkably, these new dof are fully determined by the regional radiative dof only. Finally, a direct link is drawn between this split and Dirac's dressed electron.

  21 citations