Tubelike Wormholes and Charge Confinement Talk at the 7th - PowerPoint PPT Presentation

Tubelike Wormholes and Charge Confinement Talk at the 7th Mathematical Physics Meeting, Belgrade, Sept 09-19, 2012 Eduardo Guendelman 1 , Alexander Kaganovich 1 , Emil Nissimov 2 , Svetlana Pacheva 2 1 Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva, Israel 2 Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria Tubelike Wormholes and Charge Confinement – p.1/42

7th Mathematical Physics Meeting, Belgrade, Sept 09-19, 2012 Background material and further development of: � E. Guendelman, A. Kaganovich, E.N. and S. Pacheva, (1) “Asymptotically de Sitter and anti-de Sitter Black Holes with Confining Electric Potential” , Phys. Lett. B704 (2011) 230-233, erratum Phys. Lett. B705 (2011) 545 ; (2) “Hiding Charge in a Wormhole” . The Open Nuclear and Particle Physics Journal 4 (2011) 27-34 ( arxiv:1108.3735 [hep-th]); (3) “Hiding and Confining Charges via ‘Tubelike’ Wormholes” . Int.J. Mod. Phys. A26 (2011) 5211-5239; (4) “Dynamical Couplings, Dynamical Vacuum Energy and Confinement/Deconfinement from R 2 -Gravity” . arxiv:1207.6775 [hep-th]. Tubelike Wormholes and Charge Confinement – p.2/42

Introduction - Overview of Talk We consider gravity (including f ( R ) -gravity) coupled to √ non-standard nonlinear gauge field system containing − f 0 − F 2 . 2 The latter is known to produce in flat space-time a QCD-like confinement . Several interesting features: � New mechanism for dynamical generation of cosmological constant due to nonlinear gauge field dynamics: Λ eff = Λ 0 + 2 πf 2 0 ( Λ 0 – bare CC, may be absent at all) ; � Non-standard black hole solutions of Reissner-Nordström-(anti-)de-Sitter type containing a constant radial vacuum electric field (in addition to the Coulomb one), in particular, in electrically neutral black holes of Schwarzschild-(anti-)de-Sitter type; Tubelike Wormholes and Charge Confinement – p.3/42

Introduction - Overview of Talk � In case of vanishing effective cosmological constant Λ eff ( i.e. , Λ 0 < 0 , | Λ 0 | = 2 πf 2 0 ) the resulting Reissner-Nordström-type black hole, apart from carrying an additional constant vacuum electric field, turns out to be non-asymptotically flat – a feature resembling the gravitational effect of a hedgehog ; � Appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds; � New “tubelike” solutions of Levi-Civita-Bertotti-Robinson type, i.e. , with space-time geometry of the form M 2 × S 2 , where M 2 is a two-dimensional anti-de Sitter, Rindler or de Sitter space depending on the relative strength of the electric field w.r.t. the coupling f 0 of the square-root gauge field term. Tubelike Wormholes and Charge Confinement – p.4/42

Introduction - Overview of Talk When in addition one or more lightlike branes are self -consistently coupled to the above gravity/nonlinear-gauge- field system (as matter and charge sources) they produce (“thin-shell”) wormhole solutions dislaying two novel physically interesting effects: � “Charge-hiding” effect - a genuinely charged matter source of gravity and electromagnetism may appear electrically neutral to an external observer – a phenomenon opposite to the famous Misner-Wheeler “charge without charge” effect; � Charge-confining “tubelike” wormhole with two “throats” occupied by two oppositely charged lightlike branes – the whole electric flux is confined within the finite-extent “middle universe” of generalized Levi-Civita-Bertotti-Robinson type – no flux is escaping into the outer non-compact “universes”. Tubelike Wormholes and Charge Confinement – p.5/42

Introduction - Overview of Talk Additional interesting features appear when we couple the “square-root” confining nonlinear gauge field system to f ( R ) -gravity with f ( R ) = R + αR 2 and a dilaton. Reformulating the model in the physical “Einstein” frame we find: � “Confinement-deconfinement” transition due to appearance of “flat” region in the effective dilaton potential; � The effective gauge couplings as well as the induced cosmological constant become dynamical depending on the dilaton v.e.v. In particular, a conventional Maxwell kinetic term for the gauge field is dynamically generated even if absent in the original theory; Tubelike Wormholes and Charge Confinement – p.6/42

Introduction - Overview of Talk � Regular black hole solution ( no singularity at r = 0 ) with confining vacuum electric field : the bulk space-time consist of two regions – an interior de Sitter and an exterior Reissner-Nordström-type (with “hedgehog asymptotics”) glued together along their common horizon occupied by a charged lightlike brane. The latter also dynamically determines the non-zero cosmological constant in the interior de-Sitter region. Tubelike Wormholes and Charge Confinement – p.7/42

√ − F 2 Introduction - Motivation for √ − F 2 ? Why ‘t Hooft has shown that in any effective quantum gauge theory, which is able to describe linear confinement phenomena, the energy density of electrostatic field configurations should be a linear function of the electric displacement field in the infrared region (the latter appearing as an “infrared counterterm”). The simplest way to realize these ideas in flat space-time: √ L ( F 2 ) = − 1 4 F 2 − f 0 � − F 2 , d 4 xL ( F 2 ) S = , (1) 2 F 2 ≡ F µν F µν , F µν = ∂ µ A ν − ∂ ν A µ , The square root of the Maxwell term naturally arises as a result of spontaneous breakdown of scale symmetry of the original scale-invariant Maxwell action with f 0 appearing as an integration constant responsible for the latter spontaneous breakdown. Tubelike Wormholes and Charge Confinement – p.8/42

√ − F 2 Introduction - Motivation for For static field configurations the model (1) yields an electric � displacement field � D = � E − f 0 E E | and the corresponding energy √ | � 2 E 2 = 1 D | 2 + f 0 2 � 2 | � 2 | � density turns out to be 1 D | + 1 4 f 2 0 , so that it √ indeed contains a term linear w.r.t. | � D | . The model (1) produces, when coupled to quantized fermions, a confining effective potential V ( r ) = − β r + γr (Coulomb plus linear one with γ ∼ f 0 ) which is of the form of the well-known “Cornell” potential in the phenomenological description of quarkonium systems in QCD. Tubelike Wormholes and Charge Confinement – p.9/42

Gravity Coupled to Confining Nonlinear Gauge Field The action ( R -scalar curvature; Λ 0 - bare CC, might be absent): √ √ � R − 2Λ 0 L ( F 2 ) = − 1 4 F 2 − f 0 � � − F 2 , d 4 x + L ( F 2 ) S = − G , (2 16 π 2 F 2 ≡ F κλ F µν G κµ G λν , F µν = ∂ µ A ν − ∂ ν A µ . The corresponding equations of motion read – Einstein eqs.: R µν − 1 2 G µν R + Λ 0 G µν = 8 πT ( F ) µν , (3) √ f 0 F µκ F νλ G κλ − 1 � � � F 2 + 2 f 0 � T ( F ) √ − F 2 µν = 1 − G µν , (4) 4 − F 2 and nonlinear gauge field eqs.: � √ � f 0 � � F κλ G µκ G νλ √ ∂ ν − G 1 − = 0 . (5) − F 2 Tubelike Wormholes and Charge Confinement – p.10/42

Static Spherically Symmetric Solutions Non-standard Reissner-Nordström-(anti-)de-Sitter-type black holes depending on the sign of the dynamically generated CC Λ eff : ds 2 = − A ( r ) dt 2 + dr 2 dθ 2 + sin 2 θdϕ 2 � A ( r ) + r 2 � , (6) √ r + Q 2 8 π | Q | f 0 − 2 m r 2 − Λ eff 3 r 2 Λ eff = 2 πf 2 A ( r ) = 1 − , 0 + Λ 0 , (7) with static spherically symmetric electric field containing apart from the Coulomb term an additional constant “vacuum” piece: F 0 r = ε F f 0 Q √ √ 2 + , ε F ≡ sign( F 0 r ) = sign( Q ) , (8) 4 π r 2 corresp. to a confining “Cornell” potential A 0 = − ε F f 0 Q 2 r + 4 π r . √ √ √ When Λ eff = 0 , A ( r ) → 1 − 8 π | Q | f 0 for r → ∞ (“hedgehog” non-flat-spacetime asymptotics). Tubelike Wormholes and Charge Confinement – p.11/42

Generalized Levi-Civita-Bertotti-Robinson Space-Times Three distinct types of static solutions of “tubelike” LCBR type with space-time geometry of the form M 2 × S 2 , where M 2 is some 2-dim manifold ((anti-)de Sitter, Rindler): ds 2 = − A ( η ) dt 2 + dη 2 dθ 2 + sin 2 θdϕ 2 � A ( η ) + r 2 � , −∞ < η < ∞ , (9) 0 1 = 4 πc 2 F 0 η = c F = const , F + Λ 0 (= const) . (10) r 2 0 (i) AdS 2 × S 2 with constant vacuum electric field | F 0 η | = | c F | : √ � 2 f 0 | c F | − Λ 0 � c 2 η 2 A ( η ) = 4 π F − ( η − Poincare patch coord) , 4 π (11) � � � provided either | c F | > f 0 Λ 0 for Λ 0 ≥ − 2 πf 2 1 + 1 + 0 or √ 2 πf 2 2 0 � 1 4 π | Λ 0 | for Λ 0 < 0 , | Λ 0 | > 2 πf 2 | c F | > 0 . Tubelike Wormholes and Charge Confinement – p.12/42