<p>We introduce the notion of higher Berry connection and curvature in the space of conformal boundary conditions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">d</mi></mrow></math> conformal field theories, related to each other by exactly marginal boundary deformations, forming a “boundary conformal manifold.” Our definition builds upon previous works on tensor networks, such as matrix product states, where the triple inner product or multiwavefunction overlap plays a key geometric role. On the one hand, our boundary conformal field theory formulation of higher Berry phase provides a new analytic tool to study families of invertible phases in condensed matter systems. On the other hand, it uncovers a new geometric structure on the moduli space of conformal boundary conditions, beyond the usual Riemannian structure defined through the Zamolodchikov metric. When the boundary conformal manifold has an interpretation as the position moduli space of a D-brane, our higher Berry connection coincides with the Neveu-Schwarz-Neveu-Schwarz (NS-NS) <i>B</i>-field in string theory. The general definition does not require such an interpretation and is formulated purely field theoretically, in terms of correlation functions of boundary-condition-changing operators. We also explore a connection between higher Berry connections and functional Berry connections in the loop spaces of boundary conformal manifolds.</p>

United States

Yichul Choi

Hyunsoo Ha

Dongyeob Kim

Japan

Yuya Kusuki

Austria

Shuhei Ohyama

Shinsei Ryu

Higher structures on boundary conformal manifolds: Higher Berry phase and boundary conformal field theory

We identify a local, gauge-invariant mechanism that generates a finite spectral scale in pure SU(3) Yang–Mills theory on a punctured three-ball. Fixing a <math altimg='si2.svg'><msub><mi mathvariant='double-struck'>Z</mi><mn>3</mn></msub></math> center sector isolates a single gauge-invariant holonomy angle whose Berry shift produces a quantum rotor with strictly nonzero level spacing. Gauss law is enforced by a covariant Dirichlet Helmholtz projector built from the Dirichlet inverse of the covariant scalar Laplacian with relative boundary conditions. The slow holonomy mode is chosen variationally as the minimizer of transverse electric energy under the holonomy constraint, yielding an inertia <italic>independent of the gauge representative</italic> with linear domain-size scaling and a controlled commutator-dominated regime. We prove projector stability and derive an adiabatic variational upper bound on the first positive Yang&#8211;Mills eigenvalue, with error controlled by the transverse vector gap of the covariant Laplacian on divergence-free one-forms. A femtometer-scale benchmark at realistic coupling gives an upper bound at a hadronic (&#8239;&#8764;&#8239;1&#8201;GeV) scale. In Wilczek&#8217;s sense this realizes &#8220;mass without mass&#8221;: no explicit mass term or Higgs field is introduced, and the nonzero level spacing is fixed by gauge invariance, topology, and the chosen center sector. The present results are derived on a finite domain; interpreting the length <italic>R</italic> in Minkowski space requires an additional physical input (e.g. as a local confinement length), which we make explicit.

Egypt

Ahmed Farag Ali

Mass without mass from a berry–shifted SU(3) holonomy rotor

We investigate the Berry phase arising from axion-photon and axion-fermion interactions. The effective Hamiltonians in both systems share the same form, enabling a unified description of the Berry phase and providing a novel perspective on axion experiments. We conceptually propose a new photon-ring experiment for axion detection. Furthermore, we demonstrate that measuring the axion-induced Berry phase offers a unique method for probing the global structure of the Standard Model gauge group and axion-related generalized symmetries.

China

Qing-Hong Cao

South Korea

Shuailiang Ge

Yandong Liu

Jun-Chen Wang

Berry phase in axion physics, SM global structure, and generalized symmetries

Modular Berry transport associates a geometric phase to a zero mode ambiguity in a family of modular operators. In holographic settings, this phase was shown to encode nontrivial information about the emergent spacetime geometry. We reformulate modular Berry transport for arbitrary von Neumann algebras, including giving a precise definition of the zero mode projection in terms of a conditional expectation. For a certain class of state perturbations, we demonstrate that the modular Berry phase gives rise to an emergent symplectic form in the large $\textit{N}$ limit, extending related results in the context of subregion/subalgebra duality. We also show that the vanishing of the Berry curvature for modular scrambling modes signals the emergence of a local Poincaré algebra, which plays a key role in the quantum ergodic hierarchy. These results provide an intriguing relation between geometric phases, modular chaos and the local structure of spacetime.

Netherlands

Jan Boer

Bahman Najian

Canada

Jeremy Heijden

Claire Zukowski

Modular chaos, operator algebras, and the Berry phase

We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations which sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects, and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES). The mathematical backbone of the SBLES is studied in a companion paper [1]. Our work further develops the theory of higher Berry phase and its bulk-boundary correspondence, and serves as a new computational tool for classifying symmetry protected topological phases.

Arun Debray

Sanath Devalapurkar

Cameron Krulewski

Yu Liu

Natalia Pacheco-Tallaj

Ryan Thorngren

A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases

A uniformly accelerated atom captures Pancharatnam-Berry phase in its quantum state and the phase factor depends on the vacuum fluctuation of the background quantum fields. We observe that the thermal nature of the fields further affects the induced phase. Interestingly the induced phase captures the exchange symmetry between the Unruh and real thermal baths. This observation further supports the claim that the Unruh thermal bath mimics a real thermal bath. Moreover for certain values of system parameters and at high temperature, the phase is enhanced compared to zero temperature situation. However the required temperature to observe the phase experimentally is so high that the detection of Unruh effect through this is not possible within the current technology.

India

Debasish Ghosh

Bibhas Ranjan Majhi

Influence of thermal bath on Pancharatnam-Berry phase in an accelerated frame

Particle collisions at the energy frontier can probe the nature of invisible dark matter via production in association with recoiling visible objects. We propose a new potential production mode, in which dark matter is produced by the decay of a heavy dark Higgs boson radiated from a heavy W′ boson. In such a model, motivated by left-right symmetric theories, dark matter would not be pair produced in association with other recoiling objects due to its lack of direct coupling to quarks or gluons. We study the hadronic decay mode via W′ → tb and estimate the LHC exclusion sensitivity at 95% confidence level to be 102 − 105 fb for W′ boson masses between 250 and 1750 GeV.

Ryan Holder

John Reddick

Matteo Cremonesi

Doug Berry

Kun Cheng

Matthew Low

Tim Tait

Daniel Whiteson

Hadronic mono-W′ probes of dark matter at colliders

In this study, we introduce and investigate a family of quantum mechanical models in 0 + 1 dimensions, known as generalized Born quantum oscillators. These models represent a one-parameter deformation of a specific system obtained by reducing the Nambu-Goto theory to 0 + 1 dimensions. Despite these systems showing significant similarities with $$ \textrm{T}\overline{\textrm{T}} $$ -type perturbations of two-dimensional relativistic models, our analysis reveals their potential as interesting regularizations of the Berry-Keating theory. We quantize these models using the Weyl quantization scheme up to very high orders in $\textit{ħ}$. By examining a specific scaling limit, we observe an intriguing connection between the generalized Born quantum oscillators and the Riemann-Siegel $\textit{θ}$ function.

Italy

Francesco Giordano

Stefano Negro

Roberto Tateo

The generalized Born oscillator and the Berry-Keating Hamiltonian

We present a new perspective on bulk reconstruction using Berry phases in the boundary conformal field theory (CFT). Our parallel transport of modular Hamiltonians is associated to a trajectory in the space of states, which we obtain from the insertion of a source in the Euclidean path integral. Using a modular version of the extrapolate dictionary and the equivalence between modular flow in the boundary and the bulk, we show that the expectation value of the modular Berry curvature on the boundary agrees with an appropriately defined bulk symplectic form associated to the entanglement wedge. In addition, we derive a quantum information metric on the space of density matrices from the Berry curvature, which is related to the canonical energy in the bulk. We also explore the case where a state change reduces to a shape change, uncovering the coadjoint orbit structure of kinematic space in higher dimensions.

Bartłomiej Czech

Jan de Boer

Ricardo Espíndola

Jeremy van der Heijden

Changing states in holography: From modular Berry curvature to the bulk symplectic form

We discuss novel aspects of the interaction of axions-like particles (ALP) with superfluids, superconductors in particular, and determine an induced Berry phase that is topologically singular and contributes to the generation of string-like structures. The latter are similar to vortices in superfluids. We suggest that measuring the currents generated by the Berry phase of ALP axions would enable the study of low mass regions of the ALP spectrum otherwise unobservable.

G. Lambiase

G. Papini

Searching for dark matter axions with Berry phase