We study the $$ T\overline{T} $$ deformation using its formulation as a CFT coupled to two-dimensional dynamical gravity. Working within the BRST formalism, we apply the intertwiner operator method to obtain a unitary “dressing” map between undeformed CFT operators and elements of the BRST cohomology of the deformed theory. We identify the resulting “dressed” operators corresponding to CFT primaries as the physical observables of the deformed theory and show that they arise from a field-dependent change of coordinates, in agreement with what is expected for the $$ T\overline{T} $$ deformation. We then give a non-perturbative definition of deformed correlation functions as BRST-invariant expectation values of dressed operators in the gauge theory. Finally, we verify that our construction reproduces known structural and perturbative results.

United Kingdom

E. Sabbata

Italy

P. Grassi

United States

M. Porrati

$$ T\overline{T} $$ deformations through BRST symmetry

In this paper we derive the effective theory for a stabilized five-dimensional warped geometry, addressing several outstanding issues in this derivation. These include allowing for a non-zero 4d cosmological constant, accounting for constraints from both the UV and IR branes, and determining how the stabilized theory responds to an energy perturbation on each brane. We show how a consistent low-energy effective theory from a stable warped solution must respect a constraint that follows from the higher-dimensional Einstein equation. Satisfying the constraint is equivalent to a having a local energy density that is the same at every point in the fifth dimension. This requires the stabilizing fields to adjust in response to a local change in energy density to allow for the same 4d curvature everywhere in the extra dimension, and in particular to satisfy both UV and IR boundary conditions with a warp factor that now depends on the nonzero cosmological constant. We show explicitly how this works in a 5d model, and how the correct 4d effective potential reproduces this behavior. We find that the cosmological constant generated from adding energy to one of the branes is unaffected by the details of the stabilization mechanism at leading order, despite the need for the stabilizing fields to adjust. In anticipation of a companion paper, we also briefly discuss how supersymmetry can be realized consistently in the 5d theory. In particular, we show how the stabilization mechanism remains consistent with sequestering, even as the supersymmetry-breaking energy is reflected in the stabilizing field throughout the bulk.

France

Severin Lüst

Michael Nee

Lisa Randall

More effective RS field theory

We prove that off-shell massless scalar three-point Feynman integrals are self-dual under Fourier transformation. This implies that a momentum space integral can be expressed as the position space integral of the same Feynman graph with transformed edge-weights (not the dual graph) if external vertices are labeled accordingly. In particular, any off-shell massless scalar three-point Feynman integral can be expressed as a graphical function. The result follows immediately from a theorem by M. Golz, E. Panzer and the author on parametric representations of position space integrals (2015), but it was only observed by X. Jiang in 2025 in the context of four-dimensional $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory. We generalize Jiang’s result and discuss the consequences of the self-duality in the context of graphical functions. In particular, we derive a new identity for graphical functions and a new twist relation for scalar integrals (Feynman periods) in $\textit{ϕ}$ theory.

Germany

Oliver Schnetz

Self-duality of massless scalar three-point amplitudes

We present a study of the inclusive charmless semileptonic $\textit{b}$ decay, $$ b\to {X}_u\ell \overline{\nu} $$ at next-to-next-to-leading order (NNLO) in perturbative QCD, with the primary aim of extracting the hadronic structure functions $\textit{W}$ at NNLO. The analysis is based on a numerical calculation of the relevant kinematic distributions using a phase-space slicing method to handle infrared-sensitive contributions from real gluon emissions. We use known results from Heavy Quark Effective Theory and Soft-Collinear Effective Theory to extract the singular terms and construct a model for the regular contributions to the structure functions at NNLO, then perform a fit to the numerical results. We use our approximate structure functions to compute various kinematic distributions and moments: the comparison with existing analytic and numerical results shows very good agreement, which is further improved including the available analytic results in the fit.

Austria

A. Broggio

Spain

B. Capdevila

A. Ferroglia

P. Gambino

Structure functions for the inclusive semileptonic $\textit{b}$-quark decay at NNLO: a semi-analytic calculation

We revisit (3, 0) and (3, 3) admissible solutions obtained using the MLDE method. We show that all (3, 0) solutions can be written in terms of a universal formula involving the $\textit{F}$ hypergeometric function that takes into account the monodromy at the elliptic points. We construct (3, 3) admissible solutions from (3, 0) CFTs using a duality due to Bantay and Gannon. This enables us to compute their modular properties such as the S-matrix and the fusion rules. We find that only 7 of the 15 known (3, 3) admissible solutions have proper fusion rules.

India

Suresh Govindarajan

Akhila Sadanandan

Jagannath Santara

Quasi-characters for three-character rational conformal field theories

We construct new families of non-toric 5d SCFTs via abelian orbifolds of the Reid Pagoda, including a surprising infinite family of rank-1 theories, that evade all known classifications. Using the McKay correspondence, we derive their BPS quivers and superpotentials. The hallmark of these theories is a novel sector we dub $\textit{Pagoda matter}$, whose vacuum expectation values obstruct the Kähler moduli. This mechanism freezes the gauge coupling to infinite value, precluding a weak-coupling limit and rendering the theories intrinsically strongly coupled. Finally, we interpret these results as 5d SCFTs deformed by non-constant flavor backgrounds.

Belgium

Andrés Collinucci

Fabrizio Monte

Mario Marco

Marina Moleti

Roberto Valandro

Non-toric 5d SCFTs from Reid’s Pagoda

We investigate families of 3d $$ \mathcal{N} $$ = 2 chiral quiver gauge theories conjectured to be dual to M2-branes probing toric SE singularities. Geometrically, these families correspond to toric diagrams without internal points. At the field theory level, the models are constructed via an un-higgsing procedure applied to non-chiral quivers. While the moduli space of these theories was shown to match M-theory expectations, determining the $\textit{N}$ scaling of the free energy remained an open problem for over a decade, with positive results emerging only very recently. In this work, we address this challenge by reformulating the three-sphere partition function as a hyperbolic hypergeometric integral. Using exact integral identities, we show that the free energy reduces at leading order in $\textit{N}$ to that of non-chiral quivers with chiral flavors, for which the $\textit{N}$ scaling is already established. Physically, this mathematical identity corresponds to the equivalence of three-sphere partition functions under a generalization of Giveon-Kutasov duality to chiral quivers.

Antonio Amariti

Giulia Lanzetti

$\textit{N}$ 3/2 scaling from 3d $$ \mathcal{N} $$ = 2 dualities: an alternative approach to chiral quivers

While $\textit{CP}$ models with analytic potentials are known to support finite-energy compact Q-ball and Q-shell solutions, their behavior in more complex Lagrangian frameworks remains a subject of active research. This work explores these non-topological structures within an extended Skyrme-Faddeev-type model that incorporates quartic derivative terms. In this context, harmonic time dependence and the presence of quartic terms constitute two independent stabilization mechanisms that allow the configurations to circumvent Derrick’s scaling argument. We investigate the necessary conditions for the existence of these solutions and analyze the influence of quartic terms on the resulting compactons. Specifically, we examine the scaling relationship between energy and Noether charge, expressed as $\textit{E}$($\textit{Q}$) ~ |$\textit{Q}$| . Our numerical analysis demonstrates that $\textit{n}$ < 1, which supports the stability of these solutions against spontaneous fission.

Brazil

E. Colaço

P. Klimas

Poland

L. Livramento

Japan

N. Sawado

S. Yanai

Compact Q-balls and Q-shells within a $\textit{CP}$ $\textit{N}$ Skyrme-Faddeev type model

We propose a new approach for studying $\textit{d}$ + 1 dimensional Euclidean Schwarzschild black holes with Hawking temperature near the Hagedorn temperature and Horowitz-Polchinski solutions. The worldsheet theory that describes some of these back-grounds is strongly coupled. We use its underlying affine SU(2) × SU(2) symmetry to continue to weak coupling, by varying the level of the current algebra from the small value relevant for black holes and HP solutions to a large value. In this limit, one can describe the dynamics by a solvable effective field theory, and the non-geometric features of the original problem are geometrized. The resulting construction is closely related to previous work on the non-abelian Thirring model, and sheds light on both problems.

Jinwei Chu

David Kutasov

From Horowitz-Polchinski to Thirring and back

We use Dwork’s deformation method to calculate the Hasse-Weil Zeta function of multi-parameter families of Calabi-Yau three and fourfolds. This information is used to identify subslices of codimension one in the complex-structure moduli space, where the Hodge structure splits in particular ways and different type IIB flux vacua emerge. We calculate the corresponding background fluxes and their potential that drives the IIB string compactification to these subslices and analyse the properties of the corresponding physical vacua. We address the question whether the subslices correspond to fixed loci of symmetries acting on the original family and whether they can be identified with consistent complex-structure moduli spaces of Picard-Fuchs systems with standard integral monodromy bases for fewer complex deformation parameters. We distinguish between supersymmetric vacua and singular subslices. In the latter case a standard geometrical basis can be expected if a physical transition leads to a smooth type II vacuum. In many cases the differential equations on the subslice are fulfilled by the restricted periods after adding an inhomogeneous term. This suggests that the resolution of the singularity provides three-chains and we indeed find that the corresponding integrals allow an integral expansion compatible with their interpretation as generating functions of disk instantons.

Paul Blesse

Janis Dücker

Albrecht Klemm

Julian Piribauer

Geometry and arithmetic of special loci in the moduli spaces of Type II string theory