We investigate entanglement islands and the Page curve in the framework of Horndeski gravity on a Karch-Randall braneworld background. In particular, treating the holographic boundary conformal field theory analytically we find that the Horndeski parameters significantly alter the behavior of the Page curve compared to standard general relativity, a feature caused by the nontrivial geometry induced by the Horndeski scalar field. Interestingly enough, the geometry far from the AdS limit plays a more significant role compared to previous studies. This suggests that Horndeski gravity introduces important modifications to the distribution of quantum information in the holographic model. Finally, we claim that holographic consistency can be used reversely to impose constraints on Horndeski gravity itself, providing a new tool for probing the validity of modified gravity theories.

Brazil

Fabiano Santos

Iran

Azerbaijan

Behnam Pourhassan

Chile

China

Greece

Emmanuel Saridakis

Ukraine

Oleksii Sokoliuk

Alexander Baransky

Türkiye

Emre Kahya

Holographic boundary conformal field theory within Horndeski gravity

In the current letter, we study isotropic static spherically symmetric gravastars without charge under the framework of braneworld gravity (dimensionally reduced RS-II braneworld with positive brane tension) using the metric potential of Kuchowicz type (which is physically acceptable, non-singular and stable) in the Mazur-Motolla conjuncture. We derived the Kuchowicz free parameters from the junction conditions assuming Schwarzschild vacuum without cosmological constant. As well, we assume that the interior is filled with Dark Energy (DE-like) fluid, shell with ultrarelativistic stiff fluid. Adopting this conditions, we probed several physical aspects of the gravastars, such as proper length, shell energy and entropy, surface redshift and adiabatic index, interior region mass.

India

P.K. Sahoo

Kuchowicz gravastars in the braneworld formalism

Defect characterizes the depth of factorization of terms in differential (cyclotomic) expansions of knot polynomials, i.e. of the non-perturbative Wilson averages in the Chern-Simons theory. We prove the conjecture that the defect can be alternatively described as the degree in  $$q^{\pm 2}$$  <math> <msup> <mi>q</mi> <mrow> <mo>±</mo> <mn>2</mn> </mrow> </msup> </math>   of the fundamental Alexander polynomial, which formally corresponds to the case of no colors. We also pose a question if these Alexander polynomials can be arbitrary integer polynomials of a given degree. A first attempt to answer the latter question is a preliminary analysis of antiparallel descendants of the 2-strand torus knots, which provide a nice set of examples for all values of the defect. The answer turns out to be positive in the case of defect zero knots, what can be observed already in the case of twist knots. This proved conjecture also allows us to provide a complete set of C-polynomials for the symmetrically colored Alexander polynomials for defect zero. In this case, we achieve a complete separation of representation and knot variables.

Russia

E. Lanina

A. Morozov

Defect and degree of the Alexander polynomial

For the spherically symmetric static traversable wormholes, supported by the Casimir energy in <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><mi>R</mi><mo>+</mo><mi>α</mi><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math> Quadratic, <math><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math> power-law Modified Gravity (MOG) theories we investigate energy conditions and dynamical stability of the wormhole solutions. Especially, we study Zero Tidal Forces (ZTF) Casimir WH's with anisotropic fluid located at the throat. By using the Casimir energy density and modified Einstein Field Equations (EFE's) we derived suitable shape functions for each modified gravity of our consideration. The stability of Casimir traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman-Oppenheimer-Voklov (MTOV) equation. Besides, we have numerically solved MTOV and derived hydrodynamical, anisotropic and extra forces, that is present due to the non-conserved stress-energy tensor. Moreover, other fundamental quantities, such as Volume Integral Quantifier and total gravitational energy were derived

Probing the existence of the ZTF Casimir wormholes in the framework of Gravity

In this manuscript, we construct generalized Ellis–Bronnikov wormholes in the context of f(R) modified theories of gravity. We consider that the matter driving the wormhole satisfies the energy conditions so that it is the effective energy–momentum tensor containing the higher-order derivatives of curvature terms that violate the null energy condition. Thus, the gravitational fluid is interpreted by the higher-order derivatives of curvature terms to represent the wormhole geometries and is fundamentally different from its counter representation in general relativity. In particular, we explore the wormhole geometries by presuming various well-known forms of Lagrangian f(R). In addition, for the seek of completeness, we discuss modified Tolman–Oppenheimer–Volkov, volume integral quantifier, and total gravitational energy.

Sanjay Mandal

P. Sahoo

Generalised Ellis–Bronnikov wormholes in f(R) gravity

We study Morris–Thorne static traversable wormhole solutions in different modified theories of gravity. We focus our study on the quadratic gravity  $$f({\mathscr {R}}) = {\mathscr {R}}+a{\mathscr {R}}^2$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>a</mi> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </mrow> </math>  , power-law  $$f({\mathscr {R}}) = f_0{\mathscr {R}}^n$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>f</mi> <mn>0</mn> </msub> <msup> <mrow> <mi>R</mi> </mrow> <mi>n</mi> </msup> </mrow> </math>  , log-corrected  $$f({\mathscr {R}})={\mathscr {R}}+\alpha {\mathscr {R}}^2+\beta {\mathscr {R}}^2\ln \beta {\mathscr {R}}$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>R</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mi>α</mi> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mi>β</mi> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> <mo>ln</mo> <mi>β</mi> <mi>R</mi> </mrow> </math>   theories, and finally on the exponential hybrid metric-Palatini gravity  $$f(\mathscr {\hat{R}})=\zeta \bigg (1+e^{-\frac{\hat{{\mathscr {R}}}}{\varPhi }}\bigg )$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mover> <mi>R</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <mi>ζ</mi> <mrow> <mo>(</mo> </mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <mover> <mi>R</mi> <mo>^</mo> </mover> <mi>Φ</mi> </mfrac> </mrow> </msup> <mrow> <mo>)</mo> </mrow> </mrow> </math>  . Wormhole fluid near the throat is adopted to be anisotropic, and redshift factor to have a constant value. We solve numerically the Einstein field equations and we derive the suitable shape function for each MOG of our consideration by applying the equation of state  $$p_t=\omega \rho $$  <math> <mrow> <msub> <mi>p</mi> <mi>t</mi> </msub> <mo>=</mo> <mi>ω</mi> <mi>ρ</mi> </mrow> </math>  . Furthermore, we investigate the null energy condition, the weak energy condition, and the strong energy condition with the suitable shape function b(r). The stability of Morris–Thorne traversable wormholes in different modified gravity theories is also analyzed in our paper with a modified Tolman–Oppenheimer–Voklov equation. Besides, we have derived general formulas for the extra force that is present in MTOV due to the non-conserved stress-energy tensor.

On the existence and stability of traversable wormhole solutions in modified theories of gravity

In this paper we study the group theoretic structures of colored HOMFLY polynomials in a specific limit. The group structures arise in the perturbative expansion of <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Chern-Simons Wilson loops, while the limit is <math><mi>N</mi><mo>→</mo><mn>0</mn></math>. The result of the paper is twofold. First, we explain the emergence of Kadomsev-Petviashvily (KP) τ-functions. This result is an extension of what we did in [1], where a symbolic correspondence between KP equations and group factors was established. In this paper we prove that integrability of the colored Alexander polynomial is due to it's relation to soliton τ-functions. Mainly, the colored Alexander polynomial is embedded in the action of the KP generating function on the soliton τ-function. Secondly, we use this correspondence to provide a rather simple combinatoric description of the group factors in term of Young diagrams, which is otherwise described in terms of chord diagrams, where no simple description is known. This is a first step providing an explicit description of the group theoretic data of Wilson loops, which would effectively reduce them to a purely topological quantity, mainly to a collection of Vassiliev invariants.

V. Mishnyakov

A. Sleptsov

Perturbative analysis of the colored Alexander polynomial and KP soliton -functions

We describe predictions for top quark pair differential distributions at hadron colliders, by combining the next-to-next-to-leading order quantum chromodynamics calculations and next-to-leading order electroweak corrections with double resummation at the next-to-next-to-leading logarithmic accuracy of threshold logarithms and small-mass logarithms. To the best of our knowledge, this is the first study to present such a combination, which incorporates all known perturbative information. Numerical results are presented for the invariant-mass distribution, transverse-momentum distribution, and rapidity distributions.

Germany

Michał Czakon

United States

Andrea Ferroglia

United Kingdom

Alexander Mitov

Davide Pagani

Andrew S. Papanastasiou

Benjamin D. Pecjak

Netherlands

Darren J. Scott

Sweden

Ioannis Tsinikos

Xing Wang

Li Lin Yang

Italy

Marco Zaro

Top quark pair production at complete NLO accuracy with NNLO+NNLL′ corrections in QCD L. L. Yang and X. Wang are supported in part by the National Natural Science Foundation of China (11975030, 11635001, 11575004). X. Wang is also supported in part by the Cluster of Excellence PRISMA+ (project ID 39083149). D. J. S. is supported under the ERC grant ERC-STG2015-677323. The work of D. P. and I. T. is supported by the Alexander von Humboldt Foundation, in the framework of the Sofja Kovalevskaja Award Project "Event Simulation for the Large Hadron Collider at High Precision". D. P. is also supported by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy – EXC 2121"Quantum Univers" – 390833306. I. T. is also supported by the Swedish Research Council under contract number 2016-05996. The research of A. M. and A. P. has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (683211) as well as from UK STFC grants ST/L002760/1 and ST/K004883/1. The work of M. C. was supported in part by a grant of the BMBF and by the Deutsche Forschungs-gemeinschaft under grant 396021762 - TRR 257
						

We discuss the relation between knot polynomials and the KP hierarchy. Mainly, we study the scaling 1-hook property of the coloured Alexander polynomial: <math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>R</mi></mrow><mrow><mi>K</mi></mrow></msubsup><mo>(</mo><mi>q</mi><mo>)</mo><mo>=</mo><msubsup><mrow><mi>A</mi></mrow><mrow><mo>[</mo><mn>1</mn><mo>]</mo></mrow><mrow><mi>K</mi></mrow></msubsup><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>|</mo><mi>R</mi><mo>|</mo></mrow></msup><mo>)</mo></math> for all 1-hook Young diagrams R. Via the Kontsevich construction, it is reformulated as a system of linear equations. It appears that the solutions of this system induce the KP equations in the Hirota form. The Alexander polynomial is a specialization of the HOMFLY polynomial, and it is a kind of a dual to the double scaling limit, which gives the special polynomial, in the sense that, while the special polynomials provide solutions to the KP hierarchy, the Alexander polynomials provide the equations of this hierarchy. This gives a new connection with integrable properties of knot polynomials and puts an interesting question about the way the KP hierarchy is encoded in the full HOMFLY polynomial.

A. Mironov

S. Mironov

Coloured Alexander polynomials and KP hierarchy

We connect two important conjectures in the theory of knot polynomials. The first one is the property $$Al_R(q) = Al_{[1]}(q^{|R|})$$ <math><mrow><mi>A</mi><msub><mi>l</mi><mi>R</mi></msub><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow><mo>=</mo><mi>A</mi><msub><mi>l</mi><mrow><mo>[</mo><mn>1</mn><mo>]</mo></mrow></msub><mrow><mo>(</mo><msup><mi>q</mi><mrow><mo>|</mo><mi>R</mi><mo>|</mo></mrow></msup><mo>)</mo></mrow></mrow></math>  for all single hook Young diagrams R, which is known to hold for all knots. The second conjecture claims that all the mixing matrices $$U_{i}$$ <math><msub><mi>U</mi><mi>i</mi></msub></math>  in the relation $$\mathcal{R}_i = U_i\mathcal{R}_1U_i^{-1}$$ <math><mrow><msub><mi>R</mi><mi>i</mi></msub><mo>=</mo><msub><mi>U</mi><mi>i</mi></msub><msub><mi>R</mi><mn>1</mn></msub><msubsup><mi>U</mi><mi>i</mi><mrow><mo>-</mo><mn>1</mn></mrow></msubsup></mrow></math>  between the ith and the first generators $$\mathcal{R}_i$$ <math><msub><mi>R</mi><mi>i</mi></msub></math>  of the braid group are universally expressible through the eigenvalues of $$\mathcal{R}_1$$ <math><msub><mi>R</mi><mn>1</mn></msub></math> . Since the above property of Alexander polynomials is very well tested, this relation provides new support to the eigenvalue conjecture, especially for $$i&gt;2$$ <math><mrow><mi>i</mi><mo>&gt;</mo><mn>2</mn></mrow></math> , when its direct check by evaluation of the Racah matrices and their convolutions is technically difficult.

Eigenvalue conjecture and colored Alexander polynomials