We introduce a novel class of defects, termed $\textit{crosscap defects}$, in conformal field theory (CFT) in general dimensions. These arise from quotienting the spacetime by a $\textit{ℤ}$ automorphism, and provide higher-codimension generalisations of CFTs on real projective space $$ \left({\mathbbm{RP}}^d\right) $$ . Crosscap defects extend along a $\textit{p}$-dimensional fixed locus of the $\textit{ℤ}$ action and preserve an $\textit{SO}$($\textit{p}$ + 1, 1) × $\textit{PO}$($\textit{d}$ – $\textit{p}$) subgroup of the conformal group. The two-point functions of operators in this setup exhibit three operator product expansion channels: bulk, image, and defect. These lead to several $\textit{crosscap crossing equations}$, which we present. We analyse conformal block decompositions and show that the blocks are identical to defect CFT blocks up to a redefinition of cross ratios. As concrete examples, we study crosscap defects in the $\textit{O}$($\textit{N}$) model at the Gaussian and Wilson-Fisher fixed points in the $\textit{ε}$-expansion. We compute explicitly the associated CFT data as a function of $\textit{p}$ and find that, unlike standard defects, displacement and tilt operators are absent for generic $\textit{p}$. They provide examples of defect conformal manifolds without exactly marginal operators.

United Kingdom

Nadav Drukker

Switzerland

Shota Komatsu

Anders Wallberg

Crosscap defects

We investigate holographic complexity within the Schwarzschild-de Sitter (SdS) black hole spacetime. Two distinct de Sitter holography prescriptions are examined: the static patch scheme restricted to the stretched horizon and the de Sitter/Conformal Field Theory (dS/CFT) correspondence scheme defined at asymptotic future and past infinities. We evaluate the Complexity equals Volume (CV) conjecture and extend the analysis to codimension-zero proposals, specifically Complexity equals Spacetime Volume (CV2.0) and Complexity equals Action (CA), through the Wheeler-DeWitt (WDW) patch we construct. The behaviors of the complexity in the static patch holography at late time and in the dS/CFT at infinite spacelike boundary coordinate are studied, respectively. We find that under both the CV and CV2.0 conjectures, the static patch holographic complexity and the dS/CFT holographic complexity consistently exhibit linear growth. Conversely, regarding the CA conjecture, the holographic complexity growth rates for both the static patch and the dS/CFT correspondence vanish. This behavior is attributed to the finiteness of the (regularized) action within the restricted WDW region. Furthermore, we find that, in the limit in which the boundary coordinate is taken to infinity, the complexity growth rate in the static patch prescription coincides with its counterpart in the dS/CFT prescription. This agreement suggests a deeper connection between the two descriptions and may point toward a unified understanding of bulk dynamics in de Sitter holography.

China

Chaoxi Fang

Canada

Jiayue Yang

Shao-Wen Wei

Ming Zhang

Robert Mann

Holographic complexity of de Sitter black holes

Neutrino oscillation among the three active neutrino flavors is well established and supported by experiments at diverse length scales and energy scales. It may be noted that five of the neutrino oscillation parameters in the three-flavor paradigm, namely the three mixing angles ($\textit{θ}$ , $\textit{θ}$ , $\textit{θ}$ ) and the two mass-squared differences $$ \left(\Delta {m}_{21}^2,\left|\Delta {m}_{31}^2\right|\right) $$ are measured to a reasonable degree of precision. The three unknowns that are expected to be deciphered in the near future are the Dirac CP phase, $\textit{δ}$, the neutrino mass ordering, and the octant of $\textit{θ}$ . The next generation of long baseline experiments, such as the Deep Underground Neutrino Experiment (DUNE), aims to resolve these unanswered questions. In the present work, by considering DUNE as an example, we assess the ability of long baseline experiments to extricate the intrinsic contribution from observables related to CP violation in scenarios with Standard Interaction (SI) and beyond. Additionally, we analyze the role of the second oscillation maximum in addressing the above mentioned questions. By carrying out event level and statistical analyses, we assess the potential of DUNE to probe CP violation effects both within and beyond the standard paradigm.

India

Rajrupa Banerjee

Jogesh Rout

Sudhanwa Patra

Poonam Mehta

CP violating signal at DUNE in presence of nonstandard interactions and the role of second oscillation maxima

To prepare for the next generation particle collider, likely to be a high-energy precision-frontier electron-positron machine, theoretical predictions must improve in tandem. One aspect in which it is necessary to build on the progress made at LEP and at low-energy $\textit{e}$ $\textit{e}$ colliders is in the modelling of initial-state QED radiation from leptons. In this paper we combine the Mc@Nlo parton shower matching method with QED resummation methods such as the electron structure function to obtain an automated, process-independent NLO-matched QED parton shower. The case of an electron-positron collider provides a particular challenge to the method due to the integrable singularity present in the lepton structure function, at variance with QCD PDFs. We develop new methods to allow a standard dipole parton shower to operate in the presence of this singularity. We validate the method by examining its dependence on infrared parameters and by verifying both the NLO-correctness, and the resummation properties, of the Mc@Nlo prediction. Finally, we present results for the case of Higgs production in association with an on-shell $\textit{Z}$ boson at two proposed FCC-ee energies, the first such predictions at EW NLO+PS accuracy.

Lois Flower

Marek Schönherr

$\textit{e}$ + $\textit{e}$ − → $\textit{ZH}$ at NLO EW matched to a QED parton shower

In this paper, we study the conformal block decomposition of Witten diagrams for $\textit{d}$-dimensional holographic CFTs in the presence of a $\textit{p}$-dimensional conformal defect. The holographic dual in this case contains a probe AdS brane embedded inside AdS . In particular, we focus on contact, tree-level exchanges and some one-loop two-point Witten diagrams, which contribute to the two-point function of CFT bulk scalar operators. We also consider a tree-level exchange diagram for a three-point function involving one CFT bulk scalar operator and two scalar operators localized on the defect. Employing the split representation of AdS propagators, adapted to the probe brane setup, we perform the direct channel conformal block decompositions of these diagrams. In the case of tree-level diagrams, we obtain explicit expressions for the OPE coefficients in the direct channel decompositions. For two-point tree-level exchange diagrams, we derive recursion relations for the coefficients in the crossed-channel block expansions and compute the seed coefficients which serve as inputs for these relations. Our explicit results for the block decomposition coefficients for tree-level Witten diagrams are potentially useful for further developing the analytic functional approach to bootstrapping two-point functions of bulk operators in general defect CFTs. We also study the crossing kernel, which encodes the bulk channel partial wave expansion of a defect channel partial wave. Using the bulk channel Lorentzian inversion formula for defect CFTs, we derive closed form expressions for this defect-to-bulk channel crossing kernel for zero-dimensional defects in $\textit{d}$ = 2, 4 dimensions and surface defects in $\textit{d}$ = 4, 6 dimensions.

Israel

Dean Carmi

Sudip Ghosh

Trakshu Sharma

Aspects of Witten diagrams for holographic defects

We study energy-energy correlators (EEC) in planar $$ \mathcal{N} $$ = 4 super Yang-Mills theory at strong ’t Hooft coupling $\textit{λ}$. We consider the EEC in states created by half-BPS operators of arbitrary dimension $\textit{p}$, and determine the corresponding event-shape function up to order $\textit{λ}$ from the worldsheet representation of the AdS Virasoro-Shapiro amplitude with Kaluza-Klein external states. For $\textit{p}$ = 2 we compute the second curvature correction, which completes the EEC through order $\textit{λ}$ ; the new contribution improves the agreement with recently derived non-perturbative bounds at intermediate coupling. We further develop a complementary method in which the strong-coupling expansion coefficients of the EEC are extracted directly from the Wilson coefficients of low-energy expansion of the AdS Virasoro-Shapiro amplitude, and find the two approaches in perfect agreement.

Max Jackson

Lecheng Ren

United States

Bo Wang

Congkao Wen

Energy-energy correlators at strong coupling

Thermal fluctuations are generally expected to destroy order and restore symmetries at sufficiently high temperatures. Recently, however, a family of scalar theories in 2 + 1 dimensions was shown to exhibit $\textit{ℤ}$ symmetry breaking that persists to arbitrarily high temperatures using a variety of approaches, including the $\textit{ϵ}$-expansion, the FRG, and large-$\textit{N}$ techniques. Although the similarities among these theories suggest that they belong to the same universality class, this connection has not been established explicitly. In this work, we fill this gap. Using large-$\textit{N}$ methods, we analytically study the biconical vector model in a range of spacetime dimensions, including 2 + 1, at leading and next-to-leading order in the 1/$\textit{N}$ expansion. We determine the RG flow, fixed-point structure, and the CFT data of the infrared theory, reproducing and extending previous results and thereby unifying the apparently distinct constructions within a common analytic framework. We derive the effective potential, establish its stable minima at zero and finite temperature, and demonstrate spontaneous $\textit{ℤ}$ symmetry breaking at arbitrarily high temperatures for large finite $\textit{N}$.

Michael Smolkin

Lev Yung

Thermal order in the biconical model

$$ T\overline{T} $$ -deformed CFTs are known to possess nonlocal Virasoro×Virasoro symmetries, whose currents depend on integration of the stress tensor. Unfortunately, these symmetries do not act in a tractable manner on the undeformed operators, which are defined by evolving local operators in the undeformed CFT on a constant-time slice using the deformed Hamiltonian. In this paper, we explicitly construct two distinct classes of operators: (i) dressed operators, which are primary with respect to the Virasoro×Virasoro symmetries, and (ii) physical operators, a new type of operator that depends on fundamental fields at specific points and is therefore local at the classical level. While dressed operators preserve the conformal symmetry structure, they are themselves nonlocal in the sense that they depend on integrated quantities. Physical operators, by contrast, depend only on local fields. Moreover, physical operators can be expressed in terms of dressed operators, and this relation can be promoted to a definition of such operators at the quantum level. This enables the use of Virasoro×Virasoro symmetries to systematically compute physical quantities such as correlation functions. We calculate the two-point correlation functions of these operators in momentum space and find that our results align with both string theory predictions and field theory calculations. Additionally, we explore the relationship between physical operators and alternative operator definitions proposed in the literature.

Liangyu Chen

Zhengyuan Du

Kangning Liu

Wei Song

Symmetries and operators in $$ T\overline{T} $$ deformed CFTs

The Monte Carlo (MC) replica method quantifies parameter uncertainties in global fits of parton distribution functions (PDFs) and Standard Model Effective Field Theory (SMEFT) Wilson coefficients by fitting a model to many noise-perturbed copies of the data and taking the empirical distribution of the best-fit parameters as the uncertainty. The method reproduces the Bayesian posterior exactly only when the model is linear in its parameters, and departs from it in the nonlinear case. We derive the leading-order distribution the method produces and compare it with the Laplace approximation of the Bayesian posterior: the two differ by a single computable matrix, the residual-weighted Hessian of the model at the best fit, whose sign and magnitude set the over- or under-estimation of the parameter uncertainties. This closed-form expression quantifies when and by how much the MC method departs from Bayesian inference. We illustrate it on two single-parameter examples solvable in closed form and point to its evaluation in full PDF and SMEFT fits as a natural next step.

Mark Costantini

Propagating data noise through the fit: the Monte Carlo replica distribution

We calculate the “kinematic” corrections $$ t/{P}_z^2 $$ and $$ {m}_N^2/{P}_z^2 $$ to the short distance expansion of gauge-invariant nonlocal quark-antiquark operators sandwiched between nucleon states with different momenta. Here $\textit{t}$ is the momentum transfer, $\textit{m}$ is the nucleon mass and $\textit{P}$ is the momentum component in the direction of the quark-antiquark separation, which is assumed to be large. These matrix elements can be calculated in lattice QCD and, at leading twist, expressed in terms of moments of the generalized parton distributions (GPDs). Our results allow one to control one of principal uncertainties in such calculations and extend their region of applicability to larger momentum transfers, which is important in the quest to access the three-dimension image of the proton. The calculated corrections turn out to be significant for a realistic lattice QCD setup.

Germany

Vladimir Braun

Hua-Yu Jiang

Finite-$\textit{t}$ and target mass corrections for the short-distance expansion of quasi(pseudo) GPDs