We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the state-operator correspondence to map the desired scaling dimensions to the semiclassical energy spectrum of periodic homogeneous field configurations on a cylinder. As concrete applications, we provide detailed analyses for the $\textit{ϕ}$ theory near four dimensions and $\textit{ϕ}$ near three dimensions, semiclassically determining the full spectrum of neutral operators transforming according to different Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.

Croatia

Oleg Antipin

Switzerland

Jahmall Bersini

Denmark

Jacob Hafjall

Giulia Muco

Italy

Francesco Sannino

Semiclassical canovaccio for composite operators

We show that, contrary to common expectations, the observed charged leptons can have a substantial mixing with new heavier fermions, at the level of 20%. This can happen, in the language of effective theories, when the effect of mixing with heavier fermions vanishes at tree level in operators of mass-dimension 6 (or it is suppressed by the small charged lepton masses), a cancellation that can be naturally ensured by symmetries. Using a model that realizes this scenario we consider all current direct and indirect constraints and show that experimental constraints on the mixing are so mild that, given the current direct limit on the mass of the heavy fermions, theoretical considerations become the leading current constraints on the mixing. We also estimate the sensitivity to the mixing at future experiments, including the high-luminosity phase of the LHC and, most notably, the FCC-ee, and FCC-hh. We find a pattern in which the reach of direct searches in hadron machines makes theoretical considerations lead the limits while the precision of lepton machines can beat these theoretical considerations. We find that the FCC can finally reach $\textit{per mille}$ precision in the mixing squared of the charged leptons.

Spain

J. Blas

C. Giuliano

Germany

G. Guedes

R. Sánchez López

J. Santiago

How large can lepton mixing be?

The emergence of the quantum $\textit{R}$-matrix in the double-scaled SYK model points to an underlying quantum group structure. In this work, we identify the quantum group 𝒰 (𝔰𝔲(1, 1)) as a subalgebra of the chord algebra. Specifically, we construct the generators of 𝒰 (𝔰𝔲(1, 1)) from combinations of operators within the chord algebra and show that the one-particle chord Hilbert space decomposes into the positive discrete series representations of 𝒰 (𝔰𝔲(1, 1)). Using the coproduct structure of the quantum group, we build the multi-particle Hilbert space and establish its equivalence with previous results defined by the chord rules. In particular, we show that the quantum $\textit{R}$-matrix acts as a swapping operator that reverses the ordering of open chords in each fusion channel while incorporating the corresponding $\textit{q}$-weighted penalty factors. This action enables an explicit derivation of the chord Yang-Baxter relation. We further explore a realization of the quantum group generators on the quantum disk, and present a novel factorization formula for the bulk gravitational wavefunction in the presence of matter. We also discuss the relation between the 𝒰 (𝔰𝔲(1, 1)) structure uncovered here and the 𝒰 (𝔰𝔩(2$\textit{,}$ ℝ)) algebra previously studied from the boundary perspective. Finally, we study the gravitational wavefunction with matter in the Schwarzian regime.

Canada

Jeremy Heijden

Netherlands

Erik Verlinde

United States

Jiuci Xu

Quantum symmetry and geometry in double-scaled SYK

We extend Nielsen’s formulation of quantum circuit complexity to include intrinsically non-invertible operations. Such gates arise from fusion with topological defect operators and remove a basic limitation of symmetry-based circuits: the inability to change superselection sectors, or in two-dimensional CFTs, conformal families. We realise fusion operations as completely positive, trace-preserving quantum channels acting between sectors, with consistency ensured by the fusion and associator data of an underlying unitary modular tensor category. In contrast to standard Nielsen circuits, non-invertible circuits lead to an optimisation problem that is no longer governed by geodesics on a continuous group manifold but instead reduces to a discrete shortest-path problem on the fusion graph of superselection sectors. We illustrate the framework in representative rational conformal field theories. Finally, we interpret fusion-induced transitions as discrete changes in boundary stress-tensor data, corresponding to shock-like defects in AdS gravity.

Saskia Demulder

Non-invertible Nielsen circuits and 3d Ising gravity

We study the structure of the Hilbert space of gauged matrix models with a global symmetry. In the first part of the paper, we focus on bosonic matrix models with U(2) gauge group and SO($\textit{d}$) global symmetry, and consider singlets under both the gauge and global symmetry. We show how such “double-gauged” matrix models can be described in terms of a simpler SO(3) single-matrix model. In the second part of the paper, we consider the so-called BMN subsector of the $$ \mathcal{N}=4 $$ SU($\textit{N}$) super Yang-Mills theory, which is closely related to the BMN matrix model. Among the 1/16 BPS operators in this sector, “non-graviton” operators were recently discovered, which are expected to relate to the microstates of supersymmetric $\textit{AdS}$ black holes. We show that a double gauging of this model, where one projects onto SU(3) R-symmetry singlets, considerably simplifies the analysis of the non-graviton spectrum. In particular, for low values of $\textit{N}$, we show that (almost) all graviton operators project out of the spectrum, while important classes of non-graviton operators remain. In the $\textit{N}$ = 3 case, we obtain a closed form expression for the superconformal index of singlet non-gravitons, which reveals structural features of their spectrum.

South Africa

Adwait Gaikwad

Tanay Kibe

Sam Leuven

Kayleigh Mathieson

To gauge or to double gauge? Matrix models, global symmetry, and black hole cohomologies

We present the derivation of an alternative representation of the real-time in-in formalism under a spatially homogeneous and time independent electric field. Because the system exhibits instability associated with pair production of particles and antiparticles, the perturbation theory should be reorganized depending on the choice of the reference vacuum. We recast the boundary wavefunctions into the quadratic self-energy-like terms in the functional integration formalism. The resulting generating functional in the modified in-in formalism leads to the propagators that resum infinite diagrams necessary to capture the vacuum-instability effects. The proper-time representations of the propagators reproduce the known expressions from the canonical operator formalism, but our derivation based on the generating functional along the closed-time path clarifies the origin of the additional proper-time contour and provides a better physical understanding. Finally, as a concrete example of the application, we compute the in-in expectation value of the vector current in a constant electric field, and find that the simple one-loop calculation captures the pair production effect.

Japan

Kenji Fukushima

Shuhei Minato

In-in formalism with resummation in a constant electric field: propagators including nontrivial boundary wavefunctions

We re-examine positivity bounds on the 2 $\textit{→}$ 2 scattering of identical massless real scalars with a novel perspective on how these bounds can be used to constrain the spectrum of UV theories. We propose that the entire space of consistent weakly-coupled (and generically non-supersymmetric) UV amplitudes is determined as a convex hull of the massive scalar amplitude and a one-parameter family of scalarless “extremal amplitudes” parameterized by the ratio of the masses of the two lightest massive states. Further, we propose that the extremal amplitudes can be constructed from a similar one-parameter set of maximally supersymmetric amplitudes, leading to the surprising possibility that the S-matrix bootstrap with maximal supersymmetry may be sufficient to determine the entire allowed space of four-point amplitudes! Finally, we show that minimal spectrum input reduces the allowed space of Wilson coefficients to small islands around the open string Dirac-Born-Infeld tree amplitude and the closed string Virasoro-Shapiro amplitude.

Justin Berman

Henriette Elvang

Nicholas Geiser

Loki Lin

Bootstrapping extremal scalar amplitudes with and without supersymmetry

We initiate a systematic framework for the analysis of analytic properties of finite Feynman integrals that are multiple polylogarithms. Based on the Feynman parameter representation in complex projective space, we make a complete classification of logarithmic singularities of the integral on its principal branch, by what we call touching configurations — a geometric relationship between the integrand singularity and linear subspaces tied to boundary elements of the integral contour. These on the one hand indicate first entries of the symbol of the integral, and on the other hand induce a special set of new integrals that we call elementary discontinuities. These elementary discontinuities are derived through an operation called bi-projection, and actual discontinuities of the integral across logarithmic branch cuts are their linear combinations. By recursively applying the same analysis to the induced integrals one can fully construct the symbol of the original integral. We explicitly show how this analysis works at one loop in a massless hexagon and a box with two massive and two massless loop propagators. This framework may naturally extend to higher-loop integrals.

China

Jianyu Gong

You Wang

Ellis Yuan

Symbols from bi-projections

To construct a BPS algebra with representations furnished by n-dimensional partitions, the first step is to construct the eigenvalue of the Cartan operators acting on them. The generating function of the eigenvalues is called the charge function. It has an important property that for each partition, the poles of the function correspond to the projection of the boxes which can be added to or removed from the partition legally. The charge functions of lower dimensional partitions, i.e., Young diagrams for 2D, plane partitions for 3D and solid partitions for 4D, are already given in the literature. In this paper, we propose an expression of the charge function for arbitrary odd dimensional partitions and have it proved for 5D case. Some explicit numerical tests for 7D and 9D case are also conducted to confirm our formula.

Shang Xiang

Hao Feng

Keyou Zhuo

Tian-Shun Chen

Kilar Zhang

Charge functions for odd dimensional partitions

We perform a systematic classification of (2+1)d Gross-Neveu-Yukawa-like models built out of one or more 4-component Dirac fermions and $\textit{M}$ scalar fields, which preserve an O($\textit{M}$) symmetry rotating the scalars. We then identify the perturbative fixed points of these models in the 4 – $\textit{ϵ}$ expansion. Our classification highlights several targets for the conformal bootstrap and reveals a new fixed point with $\textit{M}$ = 3, which we call the “orthogonal Heisenberg” CFT.

Matthew Mitchell

David Poland

Classifying GNY-like models