Motivated by a new term-wise factorised formula for the two-loop MHV integrand for scattering amplitudes in $$ \mathcal{N} $$ = 4 super Yang-Mills (SYM), together with recent results for the five-point negative ladders in loop space, we present the canonical forms for general ladders in loop space for an arbitrary number of particles to all loops. We make use of the graphical notation introduced in the negative geometries literature, where each loop momentum is represented as a vertex, and mutual positivity (resp. negativity) conditions as a positive (resp. negative) edge. In this paper we extend this notation to include the notion of chambers of the one-loop momentum amplituhedron. Equipped with this new graphical notation, we find the canonical form of the $\textit{L}$-loop (negative/positive) ladders for all MHV amplitudes. Our final formula is remarkably simple and reminiscent of the chiral pentagon expansion of the one and two loop momentum amplituhedron. It expresses ladder contributions as sums over maximal cuts, with each term appearing in the sum factorising into products of either chiral pentagons or their simple generalisations.

United Kingdom

Ross Glew

Tomasz Łukowski

Positive and negative ladders in loop space

In this article, we investigate the BPS invariants associated with framed links. We extend the relationship between the algebraic curve (i.e. dual $\textit{A}$-polynomial) and the BPS invariants of a knot investigated in [14] to the case of a framed knot. With the help of the framing change formula for the dual $\textit{A}$-polynomial of a framed knot, we give several explicit formulas for the extremal $\textit{A}$-polynomials and the BPS invariants of framed knots. As to the framed links, we present several numerical calculations for the Ooguri-Vafa invariants and BPS invariants for framed Whitehead links and Borromean rings and verify the integrality property for them.

China

Kai Wang

Shengmao Zhu

BPS invariants from framed links

The default way of proving holographic entropy inequalities is the contraction method. It divides Ryu-Takayanagi (RT) surfaces on the ‘greater than’ side of the inequality into segments, then glues the segments into candidate RT surfaces for terms on the ‘less than’ side. Here we discuss how proofs by contraction are constrained and informed by entanglement wedge nesting (EWN)—the property that enlarging a boundary region can only enlarge its entanglement wedge. We propose that: (i) all proofs by contraction necessarily involve candidate RT surfaces, which violate EWN; (ii) violations of EWN in contraction proofs of maximally tight inequalities occur commonly and — where this can be quantified — with maximal density near boundary conditions; (iii) the non-uniqueness of proofs by contraction reflects inequivalent ways of violating EWN. As evidence and illustration, we study the recently discovered infinite families of holographic entropy inequalities, which are associated with tessellations of the torus and the projective plane. We explain the logic, which underlies their proofs by contraction. We find that all salient aspects of the requisite contraction maps are dictated by EWN while all their variable aspects set the scheme for how to violate EWN. We comment on whether the tension between EWN and contraction maps might help in characterizing maximally tight holographic entropy inequalities.

Bartłomiej Czech

Sirui Shuai

Nesting is not contracting

Scalar particles that couple to two up quarks may be produced at the LHC even if they are ultraheavy, in the 8 − 10 TeV mass range. A renormalizable theory that includes a diquark particle of this type ($\textit{S}$ ), two vectorlike quarks ($\textit{χ}$ , $\textit{χ}$ ), and a gauge-singlet pseudoscalar, predicts LHC signals involving four or more jets of very high $\textit{p}$ . Two remarkable events observed by the CMS experiment, each involving four high-$\textit{p}$ jets, may be due to an $\textit{S}$ of mass near 8.5 TeV, and a $\textit{χ}$ mass of 2.1 TeV. A separate excess reported by CMS in the nonresonant dijet pair search is consistent with a $\textit{χ}$ mass of 0$\textit{.}$95 TeV. This hypothesis may be tested through CMS and ATLAS searches for signals with a pair of dijet resonances of masses clustered around 1 TeV, and separately around 2 TeV, which have 4$\textit{j}$ invariant masses in the 5 − 8 TeV range. These additional signals would arise from cascade decays of $\textit{S}$ → $\textit{χ}$ $\textit{χ}$ , which lead to 5$\textit{j}$ and 6$\textit{j}$ events with invariant masses around 8 TeV. Depending on the couplings of the heavy colored particles, additional signals are possible, involving for example highly-boosted top quarks.

United States

Bogdan Dobrescu

TeV-scale particles and LHC events with dijet pairs

We discuss the construction of boundary contributions to free string field theory actions in the context of the bosonic string. We show that it is generally possible to obtain a well-defined variational principle by adding a simple boundary term (which only depends on the value of the bulk fields at the boundary) to the original bulk action. However, it is in general not possible to do this in a gauge-invariant way unless suitable boundary degrees of freedom are added. We explicitly construct such boundary contributions for the massless level of both the open and the closed SFT, as well as for the tensionless limit of the full string field theory. Our results reproduce linearized general relativity with the Gibbons-Hawking-York term and provide similar gauge-invariant actions for the infinite tower of massless higher-spin gauge theories for all Regge trajectories. By writing down a gauge-invariant action for the first massive level of the open string, we provide evidence that an analogous construction should be possible for the full tensile string field theory.

Italy

Carlo Maccaferri

Czechia

Riccardo Poletti

Alberto Ruffino

France

Jakub Vošmera

Boundary modes in string field theory

Energy-momentum tensor in general conformal field theories have improvement ambiguity and it can affect the argument in deriving c-theorem. While the derivation of Zamolodchikov’s c-theorem is still formally valid with the improved energy-momentum tensor, the behavior of the c-function proposed by Zamolodchikov becomes different. When the theory suffers an IR divergence due to the non-compactness, the c-function can be unbounded and may even show non-monotonicity. We find that one of the three-point function sum rule proposed by Hartman and Mathys motivated by the averaged null energy condition, however, is agnostic about the improvement and gives the (effective) Virasoro central charge, when the IR theory is gapped.

Japan

Nanami Nakamura

Yu Nakayama

c-theorem and improvement in non-compact conformal field theories

We examine the behavior of the entanglement asymmetry in the ground state of a (1+1)-dimensional conformal field theory with a boundary condition that explicitly breaks a bulk symmetry. Our focus is on the asymmetry of a subsystem $\textit{A}$ originating from the symmetry-breaking boundary and extending into a semi-infinite bulk. By employing the twist field formalism, we derive a universal expression for the asymmetry, showing that the asymptotic behavior for large subsystems is approached algebraically, with an exponent which is twice the conformal dimension of a boundary condition-changing operator. As a secondary result, we also establish a similar asymptotic behavior for the string order parameter. Our exact analytical findings are validated through numerical simulations in the critical Ising and 3-state Potts models.

Michele Fossati

Colin Rylands

Pasquale Calabrese

Entanglement asymmetry in CFT with boundary symmetry breaking

We present significant evidence that the powerful property of Yangian invariance extends to a new large class of conformally invariant Feynman integrals. Our results apply to planar Feynman diagrams in any spacetime dimension dual to an arbitrary network of intersecting straight lines on a plane (Baxter lattice), with propagator powers determined by the geometry. We formulate Yangian symmetry in terms of a chain of Lax operators acting on the fixed coordinates around the graph, and we also extend this construction to the case of infinite-dimensional auxiliary space. Yangian invariance leads to new differential and integral equations for individual, highly nontrivial, Feynman graphs, and we present them explicitly for several examples. The graphs we consider determine correlators in the recently proposed loom fishnet CFTs. We also describe a generalization to the case with interaction vertices inside open faces of the diagram. Our construction unifies and greatly extends the known special cases of Yangian invariance to likely the most general family of integrable scalar planar graphs.

Vladimir Kazakov

Fedor Levkovich-Maslyuk

Russia

Victor Mishnyakov

Integrable Feynman graphs and Yangian symmetry on the loom

Germany

G. Buchalla

M. Capozi

A. Celis

G. Heinrich

Australia

L. Scyboz

Erratum: Higgs boson pair production in non-linear Effective Field Theory with full $\textit{m}$

We show that scale-invariant special Kähler geometries whose generic $\textit{r}$ dim abelian variety fiber is isomorphic (completely split) or isogenous (completely iso-split) as a complex torus to the product of $\textit{r}$ one-dimensional complex tori have constant $\textit{τ}$ modulus on the Coulomb branch, i.e. are isotrivial. These simple results are useful in organizing the classification of scale-invariant special Kähler geometries, which, in turn, is relevant to the classification of possible 4-dimensional $$ \mathcal{N} $$ = 2 supersymmetric superconformal field theories.