Fortschritte Der Physik-Progress of Physics最新文献

{"title":"Gravitational Deflection of Massive Body Around Global Monopole","authors":"Farook Rahaman,&nbsp;Ruhul Amin,&nbsp;Mahmud Hasan,&nbsp;Anikul Islam,&nbsp;Saibal Ray,&nbsp;Abdul Aziz,&nbsp;Naeem Ahmad Pundeer","doi":"10.1002/prop.202400007","DOIUrl":"https://doi.org/10.1002/prop.202400007","url":null,"abstract":"<p>The non-minimally coupled global monopole is a point like topological defect that may have been created during the phase transitions in the early universe. It is argued that topological defects are responsible for the structure formation of the galaxies and monopole could be the galactic dark matter in the spiral galaxies. In this article, the deflection of massive particle by the global monopole is studied. This basically makes sense as global monopole produces strong gravitational field due to enormous energy density allied with the Nambu–Goldstone field adjoining the monopole. The energy density of the monopole is decreasing with distance as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>r</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>+</mo>\u0000 <mn>0</mn>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>r</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$ r^{-2} + 0(r^{-2})$</annotation>\u0000 </semantics></math> and as a result global monopole structure plays an important role to explain the flatness of rotation curves of the outer region of various galaxies.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 1-2","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143117299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Issue Information: Fortschritte der Physik 12 / 2024","authors":"","doi":"10.1002/prop.202400909","DOIUrl":"https://doi.org/10.1002/prop.202400909","url":null,"abstract":"","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 12","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.202400909","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Notes on Characterizations of 2d Rational SCFTs: Algebraicity, Mirror Symmetry, and Complex Multiplication","authors":"Abhiram Kidambi,&nbsp;Masaki Okada,&nbsp;Taizan Watari","doi":"10.1002/prop.202400161","DOIUrl":"https://doi.org/10.1002/prop.202400161","url":null,"abstract":"<p>S. Gukov and C. Vafa proposed a characterization of rational <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$N=(1,1)$</annotation>\u0000 </semantics></math> superconformal field theories (SCFTs) in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$1+1$</annotation>\u0000 </semantics></math> dimensions with Ricci-flat Kähler target spaces in terms of the Hodge structure of the target space, extending an earlier observation by G. Moore. The idea is refined, and a conjectural statement on necessary and sufficient conditions for such SCFTs to be rational is obtained, which is indeed proven to be true in the case the target space is <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>T</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <annotation>$T^4$</annotation>\u0000 </semantics></math>. In the refined statement, the algebraicity of the geometric data of the target space turns out to be essential, and the Strominger–Yau–Zaslow fibration in the mirror correspondence also plays a vital role.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 1-2","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.202400161","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143118436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of Tachyonic Instability on the Schwinger Effect by Axial Coupling in Natural Inflation Model When Strong Back-Reaction Exists","authors":"Mehran Kamarpour","doi":"10.1002/prop.202400154","DOIUrl":"https://doi.org/10.1002/prop.202400154","url":null,"abstract":"&lt;p&gt;The influence of tachyonic instability on the Schwinger effect is investigated by axial coupling in the natural single-field inflation model when strong back-reaction exists in two parts. First, the Schwinger effect is considered when the conformal invariance of Maxwell action should be broken by axial coupling &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msup&gt;\u0000 &lt;mover&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;∼&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ I(phi)F_{mu nu }tilde{F}^{mu nu }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with the inflaton field by identifying the standard horizon scale &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ k=aH$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; at the very beginning of inflation for additional boundary term and use several values of coupling constant &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$ chi _{1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and estimate electric and magnetic energy densities and energy density of produced charged particles due to the Schwinger effect. It has been found that for both coupling functions the energy density of the produced charged particles due to the Schwinger effect is so high and spoils inflaton field. In fact the strong coupling or back-reaction occurs because the energy density of produced charged particles is exceeding of inflaton field. Two coupling functions are used to break conformal invariance of maxwell action. The simplest coupling function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mfrac&gt;\u0000 ","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 1-2","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Double Copy From Tensor Products of Metric BV■-Algebras","authors":"Leron Borsten,&nbsp;Branislav Jurčo,&nbsp;Hyungrok Kim,&nbsp;Tommaso Macrelli,&nbsp;Christian Saemann,&nbsp;Martin Wolf","doi":"10.1002/prop.202300270","DOIUrl":"https://doi.org/10.1002/prop.202300270","url":null,"abstract":"<p>Field theories with kinematic Lie algebras, such as field theories featuring color–kinematics duality, possess an underlying algebraic structure known as BV^{<span>■</span>}-algebra. If, additionally, matter fields are present, this structure is supplemented by a module for the BV^{<span>■</span>}-algebra. The authors explain this perspective, expanding on our previous work and providing many additional mathematical details. The authors also show how the tensor product of two metric BV^{<span>■</span>}-algebras yields the action of a new syngamy field theory, a construction which comprises the familiar double copy construction. As examples, the authors discuss various scalar field theories, Chern–Simons theory, self-dual Yang–Mills theory, and the pure spinor formulations of both M2-brane models and supersymmetric Yang–Mills theory. The latter leads to a new cubic pure spinor action for 10-dimensional supergravity. A homotopy-algebraic perspective on colour–flavour-stripping is also given, obtain a new restricted tensor product over a wide class of bialgebras, and it is also show that any field theory (even one without colour–kinematics duality) comes with a kinematic <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$L_infty$</annotation>\u0000 </semantics></math>-algebra.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 1-2","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.202300270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143114655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometric Relational Framework for General-Relativistic Gauge Field Theories","authors":"Jordan T. François,&nbsp;Lucrezia Ravera","doi":"10.1002/prop.202400149","DOIUrl":"https://doi.org/10.1002/prop.202400149","url":null,"abstract":"<p>It is recalled how relationality arises as the core insight of general-relativistic gauge field theories from the articulation of the generalized hole and point-coincidence arguments. Hence, a compelling case for a manifestly relational framework ensues naturally. A formulation for such a framework is proposed, based on a significant development of the dressing field method of symmetry reduction. A version for the group <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>Aut</mo>\u0000 <mo>(</mo>\u0000 <mi>P</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$operatorname{Aut}(P)$</annotation>\u0000 </semantics></math> of automorphisms of a principal bundle <span></span><math>\u0000 <semantics>\u0000 <mi>P</mi>\u0000 <annotation>$P$</annotation>\u0000 </semantics></math> over a manifold <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math> is first developed, as it is the most natural and elegant, and as <span></span><math>\u0000 <semantics>\u0000 <mi>P</mi>\u0000 <annotation>$P$</annotation>\u0000 </semantics></math> hosts all the mathematical structures relevant to general-relativistic gauge field theory. However, as the standard formulation is local, on <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$M$</annotation>\u0000 </semantics></math>, the relational framework for local field theory is then developed. The generalized point-coincidence argument is manifestly implemented, whereby the physical field-theoretical degrees of freedoms co-define each other and define, coordinatize, the physical spacetime itself. Applying the framework to General Relativity, relational Einstein equations are obtained, encompassing various notions of “scalar coordinatization” à la Kretschmann–Komar and Brown–Kuchař.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 1-2","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.202400149","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143113613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Issue Information: Fortschritte der Physik 11 / 2024","authors":"","doi":"10.1002/prop.202400908","DOIUrl":"https://doi.org/10.1002/prop.202400908","url":null,"abstract":"","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 11","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/prop.202400908","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142707531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SUSY QED with Lorentz-Asymmetric Fermionic Matter and a Glance at the Electron's EDM","authors":"João Paulo S. Melo,&nbsp;Wagno Cesar e Silva,&nbsp;José A. Helayël-Neto","doi":"10.1002/prop.202400203","DOIUrl":"https://doi.org/10.1002/prop.202400203","url":null,"abstract":"<p>This contribution sets out to pursue the investigation of a supersymmetric electrodynamics model with Lorentz-symmetry violation (LSV) manifested by a space-time unbalance in the propagation of the fermionic charged matter. Despite violation of Lorentz symmetry, the supersymmetry algebra is kept untouched. A superspace approach is then adopted to build up an <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$mathcal {N}=1$</annotation>\u0000 </semantics></math>-supersymmetric Abelian gauge theory in presence of a Lorentz-violating background supermultiplet that accommodates the space-time asymmetry parameter of the charged matter. It is described, in this scenario, how the particular Lorentz-symmetry breaking, brought about by the fermionic matter, affects its (matter) scalar partners and the photon/photino that minimally couple to charged matter. From the (modified) Dirac, Klein–Gordon and Maxwell field equations, the corresponding dispersion relations are worked out to inspect and discuss the physical effects of the LSV Majorana fermion condensates that naturally emerge from the background supermultiplet. Finally, efforts are targeted to investigate the Gordon decomposition of the charged lepton electromagnetic current. This is carried out by iterating the (fermion and scalar) matter field equations, which points to an effective contribution to the electron's electric dipole moment. This result allows us to attain an estimate of the pseudo-vector condensate of the (LSV) Majorana background fermion.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"73 1-2","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143112712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Braided Scalar Quantum Electrodynamics","authors":"Marija Dimitrijević Ćirić,&nbsp;Biljana Nikolić,&nbsp;Voja Radovanović,&nbsp;Richard J. Szabo,&nbsp;Guillaume Trojani","doi":"10.1002/prop.202400190","DOIUrl":"https://doi.org/10.1002/prop.202400190","url":null,"abstract":"<p>We formulate scalar electrodynamics in the braided <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$L_infty$</annotation>\u0000 </semantics></math>-algebra formalism and study its perturbative expansion in the algebraic framework of Batalin–Vilkovisky quantization. We also confirm that UV/IR mixing is absent at one-loop order in this noncommutative field theory, and that the non-anomalous Ward-Takahashi identities for the braided gauge symmetry are satisfied.</p>","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 12","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A\u0000 d\u0000 \u0000 S\u0000 3\u0000 \u0000 ×\u0000 \u0000 S\u0000 3\u0000 \u0000 \u0000 $AdS_3 times S^3$\u0000 Background From Poisson–Lie T-Duality","authors":"Ali Eghbali","doi":"10.1002/prop.202400175","DOIUrl":"https://doi.org/10.1002/prop.202400175","url":null,"abstract":"&lt;p&gt;The author proceed to construct a dual pair for the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$AdS_3 times S^3$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; background by applying non-Abelian T-duality (here as Poisson–Lie [PL] T-duality on a semi-Abelian double). By using a certain parametrization of the 4-dimensional Lie group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;⊗&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${A}_2 otimes 2{A}_1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and by a suitable choice of spectator-dependent matrices the original &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-model including the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$AdS_3 times S^3$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; metric and a non-trivial &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;annotation&gt;$B$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-field are constructed. The dual background constructed by means of the PL T-duality with the spectators is an asymptotically flat one with a potential black hole interpretation supported by a non-trivial &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-flux whose metric contains the true singularity with a single horizon. The question of classical integrability of the non-Abelian T-dual &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-models under consideration is addressed, and their corresponding Lax pairs are found, depending on some spectral parameters. Finally, the conformal invariance conditions of the models are checked up to two-loop order, and it has been concluded that the resulti","PeriodicalId":55150,"journal":{"name":"Fortschritte Der Physik-Progress of Physics","volume":"72 12","pages":""},"PeriodicalIF":5.6,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}