<p>We establish a precise formula relating the world sheet integral of the anti–de Sitter (AdS) Virasoro-Shapiro amplitude to the energy-energy correlator (EEC) in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> super Yang-Mills theory at strong coupling. This mapping allows us to evaluate the coefficients of the AdS curvature expansion of the EEC in terms of the world sheet integral over a unit disk. To illustrate this idea, we explicitly compute the flat-space contribution and the first curvature correction to the EEC. Our results provide a rigorous description of the stringy energy flow, demonstrating how world sheet correlators imprint themselves on collider observables and offering a potential template for effective string descriptions of energy correlators in general gauge theories.</p>

United Kingdom

Lecheng Ren

China

Bo Wang

Congkao Wen

Energy-energy correlator from the AdS Virasoro-Shapiro amplitude

The Schwinger effect, a non-perturbative mechanism for particle production in strong fields, plays a crucial role in understanding quantum vacuum decay and high-energy phenomena, including heavy-ion collisions (HIC). Although holographic quantum chromodynamics (QCD) models have been widely used to study this effect, most treatments assume isotropy or consider only a single type of anisotropy, neglecting the interplay between spatial and magnetic anisotropies that arise in realistic HIC scenarios. A unified framework accounting for both anisotropies is needed to accurately model particle production. We investigate the Schwinger effect in a twice anisotropic holographic QCD model incorporating both spatial and magnetic anisotropies. Using the anti-de Sitter/conformal field theory correspondence, we compute the total potential of a particle-antiparticle pair to quantify how these anisotropies influence pair production. Our results show that the magnetic field (parameterized by $c_B$ and $q_3$ ) enhances the Schwinger effect by lowering and narrowing the potential barrier, while increasing spatial anisotropy (controlled by $\nu$ ) suppresses the process by raising and widening the barrier. These findings demonstrate that magnetic and spatial anisotropies exert competing effects on particle production, emphasizing the necessity of treating both concurrently in holographic models. This work advances the theoretical description of the Schwinger effect in anisotropic environments, with implications for understanding non-equilibrium dynamics in HIC and other strongly coupled systems.

Wen-Bin Chang

Defu Hou

Schwinger effect in a twice anisotropic holographic model * Defu Hou's research is supported in part by the National Key Research and Development Program of China (2022YFA1604900). Additionally, Defu Hou receives partial support from the National Natural Science Foundation of China (NSFC) (12435009, 12275104). Wen-Bin Chang is supported by the Ph.D. Research Startup Project at Hubei Minzu University (RZ2500000857)

<p>In four dimensions, it has long been established that gravity coupled to matter exhibits ultraviolet divergences at one loop, irrespective of supersymmetry. Notably, the four-matter one-loop amplitudes of half-maximal supergravity coupled to Maxwell multiplets were shown in the 1970s to be divergent. Surprisingly, we demonstrate in this Letter that half-maximal theories can nevertheless become one-loop finite when uplifted to higher dimensions, contrary to naive expectations. Specifically, we study the ultraviolet properties of the four-matter and two-matter two-graviton amplitudes in six-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mo stretchy="false">(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo stretchy="false">)</mo></mrow></math> supergravities, coupled to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>T</mi></msub></math> tensor and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>V</mi></msub></math> vector multiplets, respectively. We find that the one-loop amplitudes are finite for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>T</mi></msub><mo>=</mo><mn>21</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>n</mi><mi>V</mi></msub><mo>=</mo><mn>20</mn></math>. This finiteness is unexpected, as symmetry-preserving counterterms do exist. Interestingly, both values exactly correspond to low-energy limits of type II string theories compactified on K3, which hints at possible origins to the surprising cancellations.</p>

Taiwan

Yu-tin Huang

Sweden

Henrik Johansson

Michele Santagata

Surprising One-Loop Finiteness of 6D Half-Maximal Supergravities

We study a class of heavy-heavy-light-light (HHLL) integrated correlators of superconformal primary operators in SU($\textit{N}$) $$ \mathcal{N} $$ = 4 super Yang-Mills theory involving two light operators from the stress-tensor multiplet and two heavy operators whose conformal dimensions are proportional to the number of colours $\textit{N}$. In the large-$\textit{N}$ limit these heavy operators are dual to sphere and AdS giant gravitons, realised holographically as D3-branes wrapping an $\textit{S}$ inside either the $\textit{S}$ or the $\textit{AdS}$ factor of the $\textit{AdS}$ × $\textit{S}$ background geometry. These HHLL correlators thus describe the scattering of two gravitons off D3-branes. In the planar limit we derive exact expressions for the HHLL integrated correlators as functions of both the ’t Hooft coupling and the giant graviton dimension. Remarkably, despite exhibiting distinct perturbative expansions at weak coupling, these integrated correlators share the same universal asymptotic series at strong coupling. We also demonstrate that a seemingly unrelated integrated correlator in a USp(2$\textit{N}$) $$ \mathcal{N} $$ = 2 gauge theory, holographically dual to gluon-graviton scattering off D7-branes, exhibits precisely the same strong coupling asymptotic series. This reveals a striking universality of D-brane scattering processes. Furthermore, we compute the exponentially suppressed corrections at strong coupling for all these observables, showing that they are precisely the non-perturbative effects that account for the differences between these integrated correlators beyond the universal asymptotic series. Finally, we comment on the resurgent properties and the holographic interpretation of these exponentially suppressed terms.

Augustus Brown

Daniele Dorigoni

Francesco Galvagno

Universality of giant graviton correlators

We study the large-charge sector of $$\mathcal{N}$$ = 4 super Yang-Mills theory (SYM) with SU($\textit{N}$) gauge group by constructing a special class of half-BPS heavy operators, termed “canonical operators”. Such operators exhibit remarkable simplicity in the large-charge ’t Hooft limit, where the dimension of the operators ∆ → ∞ with $${\Delta g}_{\text{YM}}^{2}$$ held finite. Canonical operator insertions in this regime map $$\mathcal{N}$$ = 4 SYM onto the Coulomb branch, by assigning a classical profile to the scalar fields with non-vanishing values along the diagonals given by the roots of unity. We follow a semiclassical approach to study two-point, three-point and Heavy-Heavy-Light-Light (HHLL) correlators. In particular we show that HHLL correlators in the large-charge ’t Hooft limit are computed as two-point functions in a background determined by the classical profiles. We provide consistent evidence of our findings by computing the same observables via supersymmetric localization.

Switzerland

Alba Grassi

Cristoforo Iossa

Large charge meets semiclassics in $$\mathcal{N}$$ = 4 super Yang-Mills

This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of bulk input data, which encompass the classifications in terms of bimodule categories. A generalized bimodule structure is introduced to capture domain-wall excitations. Furthermore, we demonstrate that folding along any GDW yields a gapped boundary (GB) described by a Frobenius algebra of the input UFC for the folded model, thus bridging our GDW classification and the GB classification in [1].

Yanyan Chen

Siyuan Wang

Yu Zhao

Yuting Hu

Yidun Wan

Classification of gapped domain walls of topological orders in 2+1 dimensions: a Levin-Wen model realization

We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges ($\textit{p}$, $\textit{q}$) in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory (SYM) with gauge group SU($\textit{N}$). An important consequence of SL(2, $\textit{ℤ}$) electromagnetic duality in $$ \mathcal{N} $$ = 4 SYM is that correlators of line defect operators with different charges ($\textit{p}$, $\textit{q}$) must be related in a non-trivial manner when the complex coupling $\textit{τ}$ = $\textit{θ}$/(2$\textit{π}$) + $$ 4\pi i/{g}_{\textrm{YM}}^2 $$ is transformed appropriately. In this work we introduce a novel class of real-analytic functions whose automorphic properties with respect to SL(2, $\textit{ℤ}$) match the expected transformations of line defect operators in $$ \mathcal{N} $$ = 4 SYM under electromagnetic duality. At large $\textit{N}$ and fixed $\textit{τ}$, the correlation functions we consider are related to scattering amplitudes of two gravitons from extended ($\textit{p}$, $\textit{q}$)-strings in the holographic dual type IIB superstring theory. We show that the large-$\textit{N}$ expansion coefficients of the integrated two-point line defect correlators are given by finite linear combinations with rational coefficients of elements belonging to this class of automorphic functions. On the other hand, for any fixed value of $\textit{N}$ we conjecture that the line defect integrated correlators can be expressed as formal infinite series over such automorphic functions. The resummation of this series produces a simple lattice sum representation for the integrated line defect correlator that manifests its automorphic properties. We explicitly demonstrate this construction for the cases with gauge group SU(2) and SU(3). Our results give direct access to non-perturbative integrated correlators in the presence of an ’t Hooft-line defect, observables otherwise very difficult to compute by other means.

Germany

Zhihao Duan

Italy

Daniele Pavarini

United States

Haitian Xie

Electromagnetic duality for line defect correlators in $$ \mathcal{N} $$ = 4 super Yang-Mills theory

We study Heavy-Heavy-Light-Light (HHLL) correlators   <math> <mfenced> <mrow> <mi>HH</mi> <msub> <mi>O</mi> <mn>2</mn> </msub> <msub> <mi>O</mi> <mn>2</mn> </msub> </mrow> </mfenced> </math>  $$ \left\langle \mathcal{HH}{\mathcal{O}}_2{\mathcal{O}}_2\right\rangle $$  in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory with SU(N) gauge group at generic N. The light operator   <math> <msub> <mi>O</mi> <mn>2</mn> </msub> </math>  $$ {\mathcal{O}}_2 $$  is the dimension two superconformal primary in the stress tensor multiplet and   <math> <mi>H</mi> </math>  $$ \mathcal{H} $$  is a general half-BPS superconformal primary operator with dimension (or R-charge)   <math> <msub> <mtext>∆</mtext> <mi>H</mi> </msub> </math>  $$ {\Delta }_{\mathcal{H}} $$ . We consider the large-charge ’t Hooft limit, where   <math> <msub> <mtext>∆</mtext> <mi>H</mi> </msub> <mo>→</mo> <mo>∞</mo> </math>  $$ {\Delta }_{\mathcal{H}}\to \infty $$  with fixed ’t Hooft-like coupling   <math> <mi>λ</mi> <mo>≔</mo> <msub> <mtext>∆</mtext> <mi>H</mi> </msub> <msubsup> <mi>g</mi> <mi>YM</mi> <mn>2</mn> </msubsup> </math>  $$ \lambda := {\Delta }_{\mathcal{H}}{g}_{\textrm{YM}}^2 $$ . We show that the L-loop contribution to the HHLL correlators in the leading large-charge limit is universal for any choice of the heavy operator   <math> <mi>H</mi> </math>  $$ \mathcal{H} $$ , given as   <math> <msup> <mi>λ</mi> <mi>L</mi> </msup> <msubsup> <mo>∑</mo> <mrow> <mi>ℓ</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>L</mi> </msubsup> <msup> <mi>Φ</mi> <mfenced> <mi>ℓ</mi> </mfenced> </msup> <msup> <mi>Φ</mi> <mfenced> <mrow> <mi>L</mi> <mo>−</mo> <mi>ℓ</mi> </mrow> </mfenced> </msup> </math>  $$ {\lambda}^L{\sum}_{\ell =0}^L{\Phi}^{\left(\ell \right)}{\Phi}^{\left(L-\ell \right)} $$  with an SU(N) colour factor coefficient, where Φ(ℓ) is the ladder Feynman integral, which is known to all loops. The dependence on the explicit form of the heavy operator lies only in the colour factor coefficients. We determine such colour factors for several classes of heavy operators, and show that the large charge limit leads to minimal powers of N. For the special class of “canonical heavy operators”, one can even resum the all-loop ladder integrals and determine the correlators at finite λ. Furthermore, upon integrating over the spacetime dependence the resulting integrated HHLL correlators agree with the existing results derived from supersymmetric localisation. Finally, as an application of the all-loop analytic results, we derive exact expressions for the structure constants of two heavy operators and the Konishi operator, finding intriguing connections with the integrated HHLL correlators.

All-loop Heavy-Heavy-Light-Light correlators in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory

We significantly extend recent work on the kinematic Hopf algebra, a structure that was shown to underlie the color-kinematics duality in Yang-Mills (YM) theory coupled to two heavy scalars, known as the heavy-mass effective theory (HEFT) limit. First, staying in the HEFT limit, we show the same kinematic Hopf algebra can be used to obtain Bern-Carrasco-Johansson (BCJ) numerators in <math><msup><mi>DF</mi><mn>2</mn></msup><mo>+</mo><mrow><mi>YM</mi></mrow></math> theory, a theory containing an infinite number of higher derivative corrections to YM, used to obtain string amplitudes via the double copy. Second, we exploit the intricate structure induced by the massive poles to obtain an efficient and direct expression for local BCJ numerators in pure YM based on the same kinematic Hopf algebra. This demonstrates that the kinematic Hopf algebra works even beyond the HEFT limit, strongly suggesting this structure universally underlies the color-kinematics duality.

Denmark

Gang Chen

Laurentiu Rodina

Kinematic Hopf algebra and Bern-Carrasco-Johansson numerators at finite <math><msup><mi>α</mi><mo>′</mo></msup></math>

We study the four-point correlator   <math> <mfenced> <mrow> <msub> <mi>O</mi> <mn>2</mn> </msub> <msub> <mi>O</mi> <mn>2</mn> </msub> <mi>DD</mi> </mrow> </mfenced> </math>  $$ \left\langle {\mathcal{O}}_2{\mathcal{O}}_2\mathcal{DD}\right\rangle $$  in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory (SYM) with SU(N) gauge group, where   <math> <msub> <mi>O</mi> <mn>2</mn> </msub> </math>  $$ {\mathcal{O}}_2 $$  represents the superconformal primary operator with dimension two, while   <math> <mi>D</mi> </math>  $$ \mathcal{D} $$  denotes a determinant operator of dimension N, which is holographically dual to a giant graviton D3-brane extending along S 5. We analyse the integrated correlator associated with this observable, obtained after integrating out the spacetime dependence over a supersymmetric invariant measure. Similarly to other classes of integrated correlators in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM, this integrated correlator can be computed through supersymmetric localisation on the four-sphere. Employing matrix-model recursive techniques, we demonstrate that the integrated correlator can be reformulated as an infinite sum of protected three-point functions with known coefficients. This insight allows us to circumvent the complexity associated with the dimension-N determinant operator, significantly streamlining the large-N expansion of the integrated correlator. In the planar limit and beyond, we derive exact results for the integrated correlator valid for all values of the ’t Hooft coupling, and investigate the resurgent properties of their strong coupling expansion. Additionally, in the large-N expansion with fixed (complexified) Yang-Mills coupling, we deduce the SL(2, ℤ) completion of these results in terms of the non-holomorphic Eisenstein series. The proposed modular functions are confirmed by explicit instanton calculations from the matrix model, and agree with expectations from the holographic dual picture of known results in type IIB string theory.

Exact results for giant graviton four-point correlators