General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett 123(3):031303, 2019), is a unitary parity-preserving model which describes two interacting spin-two fields in three-dimensional spacetime. Adopting a symplectic viewpoint, we investigate the dynamical structure of general exotic bi-gravity theory. In particular, by exploiting the properties of the corresponding pre-symplectic matrix and its associated zero-modes, we explicitly derive all constraints of the theory, including the integrability conditions and scalar relationships between all the parameters and fields defining the model. Then, as an application, these scalar relationships are used for studying the anti-de Sitter background. After that, we derive the gauge transformations for the dynamical variables from the structure of the remaining zero-modes, meaning that such zero-modes are indeed the generators of the gauge symmetry of the theory. Finally, by switching off one of the four coupling constants  $$\beta _{n}$$  <math> <msub> <mi>β</mi> <mi>n</mi> </msub> </math>   and assuming the invertibility of some of the dreibeins, we find that the general exotic bi-gravity theory has two physical degrees of freedom.

Mexico

Omar Rodríguez-Tzompantzi

Faddeev–Jackiw Hamiltonian formulation for general exotic bi-gravity

We compute the first twenty moments of three convergent quartic bi-tracial 2-matrix ensembles in the large N limit. These ensembles are toy models for Euclidean quantum gravity originally proposed by John Barrett and collaborators. A perturbative solution is found for the first twenty moments using the Schwinger-Dyson equations and properties of certain bi-colored unstable maps associated to the model. We then apply a result of Guionnet et al. to show that the perturbative and convergent solution coincide for a small neighbourhood of the coupling constants. For each model we compute an explicit expression for the free energy, critical points, and critical exponents in the large N limit. In particular, the string susceptibility is found to be γ = 1/2, hinting that the associated universality class of the model is the continuous random tree.

Canada

Masoud Khalkhali

Nathan Pagliaroli

Coloured combinatorial maps and quartic bi-tracial 2-matrix ensembles from noncommutative geometry

We formulate a version of the double copy for classical fields in curved spacetimes. We provide a correspondence between perturbative solutions to the bi-adjoint scalar equations and those of the Yang-Mills equations in position space. At the linear level, we show that there exists a map between these solutions for maximally symmetric spacetime backgrounds, that provides every Yang-Mills solution by the action of an appropriate differential operator on a bi-adjoint scalar solution. Given the existence of a linearized map, we show that it is possible to cast the solutions of the Yang-Mills equations at arbitrary perturbation order in terms of the corresponding bi-adjoint scalar solutions. This all-order map is reminiscent of the flat space BCJ double copy, and works for any curved spacetime where the perturbative expansion holds. We show that these results have the right flat space limit, and that the correspondence is agnostic to the choice of gauge.

India

Siddharth Prabhu

The classical double copy in curved spacetimes: perturbative Yang-Mills from the bi-adjoint scalar

Continuing the previous initiatives [1, 2], we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm generating two bi-orthogonal Krylov spaces, which individually generate non-orthogonal subspaces. Unlike the previously studied Arnoldi iteration, this algorithm renders the Lindbladian into a purely tridiagonal form, thus opening up a possibility to study a wide class of dissipative integrable and non-integrable systems by computing Krylov complexity at late times. Our study relies on two specific systems, the dissipative transverse-field Ising model (TFIM) and the dissipative interacting XXZ chain. We find that, for the weak coupling, initial Lanczos coefficients can efficiently distinguish integrable and chaotic evolution before the dissipative effect sets in, which results in more fluctuations in higher Lanczos coefficients. This results in the equal saturation of late-time complexity for both integrable and chaotic cases, making the notion of late-time chaos dubious.

Poland

Aranya Bhattacharya

Japan

Pratik Nandy

Pingal Nath

Himanshu Sahu

On Krylov complexity in open systems: an approach via bi-Lanczos algorithm

We study integrable deformations of two-dimensional non-linear σ-models and present a new class of classical solutions to critical bi-Yang-Baxter models for general groups. For the simplest example, namely the SL(2, ℝ) bi-Yang-Baxter model, we show that our solutions can be mapped to the known complex uniton solutions of the SU(2) bi-Yang-Baxter model. In general, our solutions are constructed from so-called Sl(2)-orbits that play a central role in the study of asymptotic Hodge theory. This provides further evidence for a close relation between integrable non-linear σ-models and the mathematical principles underlying Hodge theory. We have also included a basic introduction to the relevant aspects of asymptotic Hodge theory and have provided some simple examples.

Netherlands

Thomas Grimm

Jeroen Monnee

Bi-Yang-Baxter models and Sl(2)-orbits

Scattering amplitudes in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills theory exhibit singularities which reflect various aspects of the cluster algebras associated to the Grassmannians Gr(4, n) and their tropical counterparts. Here we investigate the potential origins of such structures and examine the extent to which they can be recovered from the Gröbner structure of the underlying Plücker ideals, focussing on the Grassmannians corresponding to finite cluster algebras.

L. Bossinger

United Kingdom

J. Drummond

R. Glew

Adjacency for scattering amplitudes from the Gröbner fan

In this paper, we construct a charged soliton with a finite energy and no delta function source in a pure Abelian gauge theory. Specifically, we first consider the three-dimensional Abelian gauge theory, with a Maxwell term and a level <math><mi>N</mi></math> CS term. We find a static solution that carries charge <math><mi>N</mi></math>, angular momentum <math><mfrac><mi>N</mi><mn>2</mn></mfrac></math> and whose radius is <math><mi>N</mi></math> independent. However, this solution has a divergent energy. In analogy to the replacement of the four-dimensional Maxwell action with the BI action, which renders the classical energy of a point charge finite, for the three-dimensional theory which includes a CS term such a replacement leads to a finite energy for the solution of above. We refer to this soliton as a CSBIon solution, representing a finite energy version of the fundamental (sourced) charged electron of Maxwell theory in four dimensions. In three dimensions the <math><mrow><mi>BI</mi><mo>+</mo><mi>CS</mi></mrow></math> action has a static charged solution with finite energy and no source, hence a soliton solution. The CSBIon, similar to its Maxwellian predecessor, has a charge <math><mi>N</mi></math>, angular momentum proportional to <math><mi>N</mi></math> and an <math><mi>N</mi></math>-independent radius. We also present other nonlinear modifications of Maxwell theory that admit similar solitons. The CSBIon may be relevant in various holographic scenarios. In particular, it may describe a D6-brane wrapping an <math><msup><mi>S</mi><mn>4</mn></msup></math> in a compactified D4-brane background. We believe that the CSBIon may play a role in condensed matter systems in <math><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> dimensions like graphene sheets.

Brazil

Horatiu Nastase

Israel

United States

Jacob Sonnenschein

Charged soliton of the three-dimensional <math><mrow><mi>CS</mi><mo>+</mo><mi>BI</mi></mrow></math> Abelian gauge theory

Integrable string sigma models on AdS3 backgrounds with 16 supersymmetries have the distinguishing feature that their superisometry group is a direct product. As a result the deformation theory of these models is particularly rich since the two supergroups in the product can be deformed independently. We construct bi-η and bi-λ deformations of two classes of ℤ 4 permutation supercoset sigma models, which describe sectors of the Green-Schwarz and pure-spinor string worldsheet theories on type II AdS3 backgrounds with pure R-R flux. We discuss an important limit of these models when one supergroup is undeformed. The associated deformed supergravity background should preserve 8 supersymmetries and is expected to have better properties than the full bi-deformation. As a step towards investigating the quantum properties of these models, we study the two-loop RG flow of the bosonic truncation of the bi-λ deformation.

Ben Hoare

France

Nat Levine

Fiona Seibold

Bi-η and bi-λ deformations of ℤ 4 permutation supercosets

We exploit the doubled formalism to study comprehensive relations among T-duality, complex and bi-hermitian structures <math><mo>(</mo><msub><mrow><mi>J</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>J</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>)</mo></math> in two-dimensional <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math> sigma models with/without twisted chiral multiplets. The bi-hermitian structures <math><mo>(</mo><msub><mrow><mi>J</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>J</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>)</mo></math> embedded in generalized Kähler structures <math><mo>(</mo><msub><mrow><mi>J</mi></mrow><mrow><mo>+</mo></mrow></msub><mo>,</mo><msub><mrow><mi>J</mi></mrow><mrow><mo>−</mo></mrow></msub><mo>)</mo></math> are organized into the algebra of the tri-complex numbers. We write down an analogue of the Buscher rule by which the T-duality transformation of the bi-hermitian and Kähler structures are apparent. We also study the bi-hypercomplex and hyperkähler cases in <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></math> theories. They are expressed, as a T-duality covariant fashion, in the generalized hyperkähler structures and form the split-bi-quaternion algebras. As a concrete example, we show the explicit T-duality relation between the hyperkähler structures of the KK-monopole (Taub-NUT space) and the bi-hypercomplex structures of the H-monopole (smeared NS5-brane). Utilizing this result, we comment on a T-duality relation for the worldsheet instantons in these geometries.

Tetsuji Kimura

Shin Sasaki

Kenta Shiozawa

Hyperkähler, bi-hypercomplex, generalized hyperkähler structures and T-duality

The bi-local fields are the quantum fields of two-particle systems, the bi-local systems, bounded by relativistic potentials. Since those form constrained dynamical systems, it is limited to introduce the interactions of the bi-local fields with other fields. In this paper, the interaction between the bi-local fields and a constant electric field E is studied with consideration for the consistency of constraints. Then, we evaluate the Schwinger effect for the bi-local systems, which gives the pair production probability of the bound states as a function of the charges of respective particles and the coupling constant in the binding potential. Through this analysis, we also discuss the possibility for the dissociation of bi-local systems due to the electric field.

Kenichi Aouda

Naohiro Kanda

Shigefumi Naka

Haruki Toyoda

Bi-local fields interacting with a constant electric field and related problems including the Schwinger effect