We study four-point correlators in superconformal theories in various dimensions. We develop an efficient method to solve the superconformal Ward identities in Mellin space. For 4d $$ \mathcal{N} $$ = 4 SYM and the 6d $$ \mathcal{N} $$ = (2$\textit{,}$ 0) theory, our method reproduces the known solutions. As novel applications of this method, we also derive solutions in 3d $$ \mathcal{N} $$ = 8 ABJM, and for two-point correlators in 4d $$ \mathcal{N} $$ = 4 SYM with line defects.

United Kingdom

Clément Virally

Solving superconformal Ward identities in Mellin space

<p>We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector (PVV) triangle graph. For the well-studied QED case, we show explicitly how the off-forward AVV pole exactly cancels an identical PVV pole. We then demonstrate the dramatic difference in QCD due to the chiral condensate, which qualitatively modifies anomalous Ward identities. As in the massless case, the anomaly pole in QCD is canceled by the dynamics of a primordial isosinglet pseudoscalar <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>η</mi><mo stretchy="false">¯</mo></mover></math>-meson, whose Wess-Zumino-Witten coupling to the topological charge density shifts the pole to the physical <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>η</mi><mo>′</mo></msup></math> mass, with the finite quark mass contribution differing by <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>O</mi><mo stretchy="false">(</mo><mn>10</mn><mo>%</mo><mo stretchy="false">)</mo></math> from the Witten-Veneziano formula. We obtain a compact analytic expression for the finite mass corrections to Shore and Veneziano’s result that the proton’s net quark helicity <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi mathvariant="normal">Σ</mi><mo>∝</mo><msqrt><mrow><msubsup><mi>χ</mi><mi>QCD</mi><mo>′</mo></msubsup><msub><mo stretchy="false">|</mo><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow></msub><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msqrt></math>, the forward slope of the topological susceptibility in the chiral limit, and show they are of the order of a few percentages. Our prior prediction that the polarized DIS structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>g</mi><mn>1</mn></msub></math> is quenched by sphaleronlike topological transitions at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math> is unaffected by quark mass effects. Our results illustrate how worldline computations of anomalous processes, in synergy with lattice computations and nonet chiral perturbation theory, can uncover novel nonperturbative features of QCD at the Electron-Ion Collider.</p>

United States

Andrey Tarasov

Raju Venugopalan

Role of the chiral anomaly in polarized deeply inelastic scattering. III. Wess-Zumino-Witten contributions and chiral Ward identities for finite quark mass

Superconformal Ward identities are revisited in the context of superconformal line defects. Multipoint correlators of topological operators inserted on superconformal lines are studied. In particular, it is known that protected operators preserving enough of the supersymmetry become topological after performing a topological twist. By definition, such a correlator is constant in the topological limit. By analysing the topological constraint on the OPE of such operators, the correlator is further constrained away from this limit. The constraints on multipoint correlators match the known superconformal Ward identities in the case of 4-point functions. This allows for an simple and universal derivation of the superconformal Ward identities governing the multipoint correlation functions of such operators. This concept is illustrated by 1/2-BPS operators with an $\textit{su}$(2) R-symmetry and further explored in the case of the displacement multiplet on the 1/2-BPS Wilson line in 4d $$ \mathcal{N} $$ = 4 super Yang-Mills theory supporting the conjectured multipoint Ward identities in the literature.

France

Gabriel Bliard

On multipoint Ward identities for superconformal line defects

Abstract The first analytic expressions for one-loop-induced contributions for the decay of CP-even Higgs H → hγγ, with  being the Standard-Model-like Higgs boson within the framework of the two-Higgs doublet model, are presented in this paper. The one-loop form factors for the decay processes are written in terms of scalar one-loop Passarino–Veltman functions following the input notations of both the LoopTools and Collier packages. Subsequently, physical results for the decay processes can be generated numerically by using one of the above-mentioned packages. The analytic expressions shown in this paper are verified by several numerical checks, e.g. the ultraviolet and infrared finiteness of the one-loop amplitude. Furthermore, the amplitude satisfies the Ward identity due to on-shell photons in final states. The identity is also checked numerically in this work. In phenomenological studies, the differential decay rates for H → hγγ as a function of the invariant mass of two photons in final states are first examined in the parameter space of the two-Higgs doublet models.

Vietnam

Khiem Hong Phan

Dzung Tri Tran

Thanh Huy Nguyen

Decay of CP-Even Higgs in the Two-Higgs Doublet Model: One-Loop Analytic Results and Ward Identity Checks

Large N quasifermionic (QF) Chern-Simons-matter theories exhibit weakly-broken higher-spin symmetry and contain an infinite-dimensional algebra of almost-conserved higher-spin currents. By analyzing local higher-spin Ward identities, we constrain the higher-spin algebra of this theory, for operators of spin s &lt; 4. The solution interpolates smoothly between Ward identities of free-fermionic and critical-bosonic U(N) models, in accordance with the bosonization duality. At finite ’t Hooft coupling, we decompose four-point current correlators involving (∂ ∙ J 3) QF  in terms of free theory structures and identify possible epsilon-transform relations for QF four-point functions. Additionally, we find that higher correlators of the theory develop scheme-independent higher-spin contact terms, stemming from the presence of a background Chern-Simons term in the effective action. These terms are related to similar contact terms of the associated quasibosonic Chern-Simons-matter theory via Legendre transform. The results are supplemented by perturbative checks, including collinear limit computations of ⟨T − − J + J +⟩ QF , ⟨T − − J + J + O⟩ QF  and ⟨J − − − J + J + J +⟩ QF .

Israel

Trivko Kukolj

Four-point functions and contact terms from higher-spin Ward identities of Chern-Simons-matter theory

This paper develops an enlarged BRST framework to treat the large gauge transformations of a given quantum field theory. It determines the associated infinitely many Noether charges stemming from a gauge fixed and BRST invariant Lagrangian, a result that cannot be obtained from Noether’s second theorem. The geometrical significance of this result is highlighted by the construction of a trigraded BRST covariant phase space, allowing a BRST invariant gauge fixing procedure. This provides an appropriate framework for determining the conserved BRST Noether current of the global BRST symmetry and the associated global Noether charges. The latter are found to be equivalent with the usual classical corner charges of large gauge transformations. It allows one to prove the gauge independence of their physical effects at the perturbative quantum level. In particular, the underlying BRST fundamental canonical relation provides the same graded symplectic brackets as in the classical covariant phase space. A unified Lagrangian Ward identity for small and large gauge transformations is built. It consistently decouples into a bulk part for small gauge transformations, which is the standard BRST-BV quantum master equation, and a boundary part for large gauge transformations. The boundary part provides a perturbation theory origin for the invariance of the Hamiltonian physical -matrix under asymptotic symmetries. Holographic anomalies for the boundary Ward identity are studied and found to be solutions of a codimension one Wess-Zumino consistency condition. Such solutions are studied in the context of extended BMS symmetry. Their existence clarifies the status of the 1-loop correction to the subleading soft graviton theorem.

Laurent Baulieu

Tom Wetzstein

BRST covariant phase space and holographic Ward identities

We derive the new identity in homotopy algebras which directly corresponds to the Schwinger-Dyson equations in quantum field theory. As an application, we derive the Ward-Takahashi identities. We demonstrate that the Ward-Takahashi identities are reproduced in several examples. In general, our formula contains divergence. We mediate this problem by introducing stubs known in the context of string field theory. With the regularization, we can calculate the anomaly such as axial U(1) anomaly in vector-like U(1) gauge theory.

Japan

Keisuke Konosu

Jojiro Totsuka-Yoshinaka

Noether’s theorem and Ward-Takahashi identities from homotopy algebras

This paper, as a continuation of our previous investigation [Nucl. Phys. B 1005 (2024) 116582] aims to study the glassy random matrices with quenched Wigner disorder. In this previous work, we have constructed a renormalization group based on the effective deterministic kinetic spectrum emerging from large N limit, and we extended approximate solutions using standard vertex expansion, at the leading order of the derivative expansion. Now in the following work, by introducing the non-trivial Ward identities which come from the <math><msup><mrow><mo>(</mo><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo><mo>)</mo></mrow><mrow><mo>×</mo><mn>2</mn></mrow></msup></math> symmetry broken of the effective kinetic action, we provide in the deep IR the explicit solution of the functional renormalization group for a model with quartic coupling by solving the Hierarchy to all orders in the local sector, which in particular imply the vanishing of the anomalous dimension. The numerical investigations confirm the first-order phase transition discovered in the vertex expansion framework, both in the active and passive schemes. Finally, we extend the discussion to hermitian matrices.

Vincent Lahoche

Benin

Dine Ousmane Samary

Functional renormalization group for “ = 2” like glassy matrices in the planar approximation II. Ward identities method in the deep IR

We introduce Ward identities for superamplitudes in D-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$ -extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for an n-partice superamplitude take a simple universal form for half BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of the n superparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by (D − 2)L + 2 −   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  or (D − 2)L + 2 −   <math> <mn>2</mn> <mi>N</mi> </math>  $$ 2\mathcal{N} $$ , respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.

Renata Kallosh

Ward identities for superamplitudes

Abstract Recently, lattice formulations of Abelian chiral gauge theory in two dimensions have been devised on the basis of the Abelian bosonization. A salient feature of these 2D lattice formulations is that the gauge invariance is exactly preserved for anomaly-free theories and thus is completely free from the question of the gauge mode decoupling. In the present paper, we propose yet another lattice formulation sharing this desired property. A particularly unique point in our formulation is that the vertex operator of the dual scalar field, which carries the vector charge of the fermion and the “magnetic charge” in the bosonization, is represented by a “hole” excised from the lattice; this is the excision method formulated recently by Abe et al. in a somewhat different context.