A novel Bogomol’nyi–Prasad–Sommerfield (BPS) bound for the Gross–Pitaevskii equations in two spatial dimensions is presented herein. The energy can be bounded from below in terms of the combination of two boundary terms, one related to the vorticity (but “dressed” by the condensate profile) and the second to the “skewness” of the configurations. The bound is saturated by configurations that satisfy a system of two first-order partial differential equations. When such a BPS system is satisfied, the Gross–Pitaevskii equations are also satisfied. The analytic solutions of this BPS system in the present manuscript represent configurations with fractional vorticity living in an annulus. Using these techniques, we present the first analytic examples of this kind. The hydrodynamic interpretation of the BPS system is discussed, and the implications of these results are outlined.

Chile

Fabrizio Canfora

Czechia

Pablo Pais

A Bogomol’nyi–Prasad–Sommerfield bound with a first-order system in the 2$\textit{D}$ Gross–Pitaevskii equation

The (generalized) Gross-Pitaevskii equation (GPE) for a complex scalar field in two spatial dimensions is analyzed. It is shown that there is an infinite family of self-interaction potentials which admit Bogomol'nyi-Prasad-Sommerfield (BPS) bounds together with the corresponding first-order BPS systems. For each member of this family, the solutions of the first-order BPS systems are automatically solutions of the corresponding second-order generalized GPE. The simplest topologically non-trivial solutions of these first-order BPS systems describe configurations with quantized fractional vorticity. The corresponding fraction is related to the degree of non-linearity. The case in which the self-interaction potential is of order six (namely <math altimg='si1.svg'><mo stretchy='false'>|</mo><mi mathvariant='normal'>&#936;</mi><msup><mrow><mo stretchy='false'>|</mo></mrow><mrow><mn>6</mn></mrow></msup></math>, which is a relevant theory both in relativistic quantum field theories in <math altimg='si2.svg'><mo stretchy='false'>(</mo><mn>2</mn><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mn>1</mn><mo stretchy='false'>)</mo></math> dimensions in connection with the quantum Hall effect as well as in the theory of the supersolids) is analyzed in detail. Such formalism can also be extended to the case of quantum mixtures with multi-component GPEs. The relationship between these techniques and supersymmetry will be discussed. In particular, despite several common features, we will show that there are multi-component GPEs that are not supersymmetric (at least, not in the standard sense) and possess a BPS system of the above type.

Fractional vorticity, Bogomol'nyi-Prasad-Sommerfield systems and complex structures for the (generalized) spinor Gross-Pitaevskii equations

<p>We compute four-point correlators in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> super-Yang-Mills theory with both single and double-particle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1</mn><mo>/</mo><mn>2</mn></math>-Bogomol’nyi-Prasad-Sommerfield (BPS) operators in the regime of large ’t Hooft coupling and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>. In particular, we give explicit expressions up to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mn>1</mn><mo>/</mo><msup><mi>N</mi><mn>4</mn></msup><mo stretchy="false">)</mo></math> for the lightest correlator with two double-particle and two single-particle operators built out of the stress-tensor multiplet. Our derivation makes use of the general holographic prescription applied to an asymptotically <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>5</mn></mrow></msub><mo>×</mo><mrow><msup><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>5</mn></mrow></msup></mrow></mrow></math> geometry that describes a coherent superposition of multigraviton operators. The final result can be written in terms of a natural generalization of the standard <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>D</mi></mrow></math> functions and takes a compact form in Mellin space. The correlator we compute here is the simplest of a more general class of correlators where two inserted operators are multiparticles. These can be derived with the same approach, suggesting that the structure found here is general.</p>

Spain

Francesco Aprile

Italy

Stefano Giusto

United Kingdom

Rodolfo Russo

Holographic Correlators with Bogomol’nyi-Prasad-Sommerfield Bound States in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></mrow></math> Supersymmetric Yang-Mills Theory

A generalized Amit-Roginsky vector model in flat space is obtained as the effective dynamics of pertubations around a classical solution of the Boulatov group field theory for 3D Euclidean quantum gravity, extended to include additional matter degrees of freedom. By further restricting the type of perturbations, the original Amit-Roginsky model can be obtained. This result suggests a general link (and possibly a unified framework) between two types of tensorial quantum field theories; on one hand quantum geometric group field theories and tensorial models for random geometry, and on the other hand melonic-dominated vector and tensorial models in flat space, such as the Amit-Roginsky model and the Sachdev-Ye-Kitaev model.

France

Victor Nador

Germany

Daniele Oriti

Xiankai Pang

Romania

Adrian Tanasa

Yi-Li Wang

Generalized Amit-Roginsky model from perturbations of 3D quantum gravity

In this study, we investigate a new relativistic anisotropic Einstein field equations solution for compact stars under embedding class 1 conditions. In order to do this, we apply the Karmarkar condition and the embedding class one technique. By taking Buchdahl type metric potential  $$ g_{rr} $$  <math> <msub> <mi>g</mi> <mrow> <mi>rr</mi> </mrow> </msub> </math>   into consideration, the precise analytical solution has been investigated. We have studied physical characteristics of various compact star using this analytical solution. Central singularities are absent from the solution. We have explored thermodynamic observables inside the stellar models, such as radial and tangential pressures, matter density, anisotropic factor, energy conditions, TOV, red-shift, and the speed of sound, etc., after establishing this space-time geometry for the stellar models. From the graphical representation of various physical characteristics, it is demonstrated that our model meets all the specification for ultra-high density compact bodies.

India

Amit Prasad

Mahesh Kumar

Jitendra Kumar

Relativistic modeling of stellar objects in a Schwarzschild’s coordinates with embedded class one spacetime

In this work, we explore a class of compact charged objects that have been tested against experimental and observational constraints with some known compact stars candidates. This study is performed by considering the self-gravitating, charged, isotropic fluids which are more pliability in solving the Einstein–Maxwell equations. In order to determine the interior geometry, we utilize the Vaidya–Tikekar (J Astrophys Astron 3:325, 1982) geometry for the metric potential with Riessner–Nordstr$$\ddot{\text {o}}$$ <math><mover><mtext>o</mtext><mo>¨</mo></mover></math> m metric as an exterior solution. These model parameters are determined after selecting some particular values of M and R, for the compact objects SAX J1808.4-3658, Her X-1 and 4U 1538-52. The most striking consequence is that hydrostatic equilibrium is maintained for different forces, and the situation is clarified by using the generalized Tolman–Oppenheimer–Volkoff equation. In addition to this, we also present the energy conditions, speeds of sound and compactness of stars that are very much compatible to that for a physically acceptable stellar model. Arising solutions are also compared with graphical representations that provide strong evidences for more realistic and viable models, both at theoretical and astrophysical scale.