Casimir effect and the quarkanti-quark potential Zolt an Bajnok , - PowerPoint PPT Presentation

Gauge/gravity duality, Munich, July 30, 2013 Casimir effect and the quark–anti-quark potential Zolt´ an Bajnok , MTA-Lend¨ ulet Holographic QFT Group, Wigner Research Centre for Physics, Hungary with L. Palla, G. Tak´ acs, J. Balog, A. Heged˝ us, G.Zs. T´ oth 1

Gauge/gravity duality, Munich, July 30, 2013 Casimir effect and the quark–anti-quark potential Zolt´ an Bajnok , MTA-Lend¨ ulet Holographic QFT Group, Wigner Research Centre for Physics, Hungary with L. Palla, G. Tak´ acs, J. Balog, A. Heged˝ us, G.Zs. T´ oth T anti−quark L quark space q time q � W � = e − TV q ¯ q ( L,λ ) = e − TE 0 ( L,λ ) extra dimension L

Gauge/gravity duality, Munich, July 30, 2013 Casimir effect and the quark–anti-quark potential Zolt´ an Bajnok , MTA-Lend¨ ulet Holographic QFT Group, Wigner Research Centre for Physics, Hungary with L. Palla, G. Tak´ acs, J. Balog, A. Heged˝ us, G.Zs. T´ oth � d ˜ p p ) e − 2 E (˜ p ) L ) E 0 ( L ) = − 2 π log(1 + R ( − ˜ p ) R (˜ d � k ( L ) ω ( k ( L )) F ( L ) = dE 0 ( L ) = dL 2 dL

Motivation: Casimir-Polder effect Hendrik Casimir Dirk Polder colloidal solution: neutral atoms force not like Van der Waals = − � cπ 2 F ( L ) A 240 L 4 not a theoretical curiosity! 2

Motivation: Casimir-Polder effect Hendrik Casimir Dirk Polder colloidal solution: neutral atoms force not like Van der Waals = − � cπ 2 F ( L ) A 240 L 4 Gecko legs not a theoretical curiosity!

Motivation: Casimir-Polder effect Hendrik Casimir Dirk Polder colloidal solution: neutral atoms force not like Van der Waals Airbag trigger chip = − � cπ 2 F ( L ) A 240 L 4 Gecko legs not a theoretical curiosity!

Motivation: Casimir-Polder effect Hendrik Casimir Dirk Polder colloidal solution: neutral atoms micromechanical force not like Van der Waals device: pieces stick Airbag trigger chip = − � cπ 2 F ( L ) friction, levitation A 240 L 4 Gecko legs not a theoretical curiosity!

Motivation: Casimir-Polder effect Hendrik Casimir Dirk Polder colloidal solution: neutral atoms micromechanical force not like Van der Waals device: pieces stick Airbag trigger chip = − � cπ 2 F ( L ) friction, levitation A 240 L 4 Gecko legs not a theoretical curiosity! Maritime analogy:

Aim: understand/describe planar Casimir effect 3

Aim: understand/describe planar Casimir effect Usual explanation: energy of the vacuum: E 0 ( L ) = 1 k ( L ) ω ( k ( L )) ∝ ∞ � 2

Aim: understand/describe planar Casimir effect Usual explanation: energy of the vacuum: E 0 ( L ) = 1 k ( L ) ω ( k ( L )) ∝ ∞ � 2 ∆ E 0 ( L ) E 0 ( L ) − E 0 ( ∞ ) − 2 E plate = ∆ E 0 ( L ) ; A

Aim: understand/describe planar Casimir effect Usual explanation: energy of the vacuum: E 0 ( L ) = 1 k ( L ) ω ( k ( L )) ∝ ∞ � 2 ∆ E 0 ( L ) E 0 ( L ) − E 0 ( ∞ ) − 2 E plate = ∆ E 0 ( L ) ; A Lifshitz formula: QED, Parallel dielectric slabs ( ǫ 1 , 1 , ǫ 2 ) � ∞ ǫ 2 ω 2 − q 2 e − 2 L √ � ω 2 − q 2 − ǫ 1 ω 2 − q 2 ω 2 − q 2 − ǫ 2 ω 2 − q 2 � � � � � d 2 q ∆ E 0 ( L ) 1 − ǫ 1 ǫ 2 q 2 + ζ 2 = 8 π 2 dζ log ω 2 − q 2 + ǫ 1 ω 2 − q 2 ω 2 − q 2 + � � � � A ǫ 1 ǫ 2 0 � ∞ ǫ 2 ω 2 − q 2 e − 2 L √ � ω 2 − q 2 − ǫ 1 ω 2 − q 2 ω 2 − q 2 − ǫ 2 ω 2 − q 2 � � � � � d 2 q q 2 + ζ 2 + 8 π 2 dζ log 1 − ω 2 − q 2 + ǫ 1 ω 2 − q 2 ω 2 − q 2 + � � � � 0

Aim: understand/describe planar Casimir effect Usual explanation: energy of the vacuum: E 0 ( L ) = 1 k ( L ) ω ( k ( L )) ∝ ∞ � 2 ∆ E 0 ( L ) E 0 ( L ) − E 0 ( ∞ ) − 2 E plate = ∆ E 0 ( L ) ; A Lifshitz formula: QED, Parallel dielectric slabs ( ǫ 1 , 1 , ǫ 2 ) � ∞ ǫ 2 ω 2 − q 2 e − 2 L √ � ω 2 − q 2 − ǫ 1 ω 2 − q 2 ω 2 − q 2 − ǫ 2 ω 2 − q 2 � � � � � d 2 q ∆ E 0 ( L ) 1 − ǫ 1 ǫ 2 q 2 + ζ 2 = 8 π 2 dζ log ω 2 − q 2 + ǫ 1 ω 2 − q 2 ω 2 − q 2 + � � � � A ǫ 1 ǫ 2 0 � ∞ ǫ 2 ω 2 − q 2 e − 2 L √ � ω 2 − q 2 − ǫ 1 ω 2 − q 2 ω 2 − q 2 − ǫ 2 ω 2 − q 2 � � � � � d 2 q q 2 + ζ 2 1 − + 8 π 2 dζ log ω 2 − q 2 + ǫ 1 ω 2 − q 2 ω 2 − q 2 + � � � � 0 L Physics can be understood in 1+1 D QFT integrability helps to solve the problem even exactly

A simple calculation e ikx −ikx R e Free bulk + interacting boundaries (QED) − −ikx e ikx R e + L E 0 ( L ) = 1 k ( L ) ω ( k ( L )) � Q ( k ) = e 2 ikL R − ( k ) R + ( − k ) − 1 = 0 2 4

A simple calculation e ikx −ikx R e Free bulk + interacting boundaries (QED) − −ikx e ikx R e + L E 0 ( L ) = 1 k ( L ) ω ( k ( L )) � Q ( k ) = e 2 ikL R − ( k ) R + ( − k ) − 1 = 0 2 C i E 0 ( L ) = 1 2 πi ω ( k ) d dk � dk log Q � j j 2 k i k

A simple calculation e ikx −ikx R e Free bulk + interacting boundaries (QED) − −ikx e ikx R e + L E 0 ( L ) = 1 k ( L ) ω ( k ( L )) � Q ( k ) = e 2 ikL R − ( k ) R + ( − k ) − 1 = 0 2 C i E 0 ( L ) = 1 2 πi ω ( k ) d dk � dk log Q � j j 2 k i k C + � dk dω ( k ) E 0 ( L ) = 1 log Q � 2 2 πi dk k i k + , − C −

A simple calculation e ikx −ikx R e Free bulk + interacting boundaries (QED) − −ikx e ikx R e + L E 0 ( L ) = 1 k ( L ) ω ( k ( L )) � Q ( k ) = e 2 ikL R − ( k ) R + ( − k ) − 1 = 0 2 C i E 0 ( L ) = 1 2 πi ω ( k ) d dk � dk log Q � j j 2 k i k C + � dk dω ( k ) E 0 ( L ) = 1 log Q � 2 2 πi dk k i k + , − C − C � dk dω ( k ) E 0 ( L ) = e bulk L + e bdry + log Q 2 πi dk k i k

A simple calculation e ikx −ikx R e Free bulk + interacting boundaries (QED) − −ikx e ikx R e + L E 0 ( L ) = 1 k ( L ) ω ( k ( L )) � Q ( k ) = e 2 ikL R − ( k ) R + ( − k ) − 1 = 0 2 C i E 0 ( L ) = 1 2 πi ω ( k ) d dk � dk log Q � j j 2 k i k C + � dk dω ( k ) E 0 ( L ) = 1 log Q � 2 2 πi dk k i k + , − C − C � dk dω ( k ) E 0 ( L ) = e bulk L + e bdry + log Q 2 πi dk k i k −i ω C � d ˜ ǫ (˜ k k ) e − 2˜ k ) L ) E ren 2 π log(1 − R − (˜ k ) R + ( − ˜ ( L ) = 0 k i k

A simple calculation e ikx −ikx R e Free bulk + interacting boundaries (QED) − −ikx e ikx R e + L E 0 ( L ) = 1 � k ( L ) ω ( k ( L )) Q ( k ) = e 2 ikL R − ( k ) R + ( − k ) − 1 = 0 2 C i E 0 ( L ) = 1 2 πi ω ( k ) d dk � � dk log Q j j 2 k i k C + � dk dω ( k ) E 0 ( L ) = 1 � log Q 2 2 πi dk k i k + , − C − C � dk dω ( k ) E 0 ( L ) = e bulk L + e bdry + log Q 2 πi dk k i k −i ω C � d ˜ ǫ (˜ k k ) e − 2˜ k ) L ) E ren 2 π log(1 − R − (˜ k ) R + ( − ˜ ( L ) = 0 k i k interacting but integrable: similar formula

Integrable boundary field theory: Bootstrap 5

Integrable boundary field theory: Bootstrap Boundary multiparticle state: with n particles �� �� v 1 v 2 �� �� > > ... > v n > 0 �� �� �� �� �� �� �� �� �� �� �� ��

Integrable boundary field theory: Bootstrap Boundary one particle state: � � v 1 � � � � � � � � � � � � � �

Integrable boundary field theory: Bootstrap Boundary one particle in state: t → −∞ � � � � v 1 � � � � � � � � � � � �

Integrable boundary field theory: Bootstrap Boundary one particle in state: t → −∞ times develop � � � � � � v 1 v 1 � � � � � � � � � � � � � � � � � � � � � � � � � �

Integrable boundary field theory: Bootstrap Boundary one particle in state: t → −∞ times develop further � � � � � � v 1 v 1 � � � � � � � � � � � � � � � � � � � � � � � � � �

Integrable boundary field theory: Bootstrap Boundary one particle in state: t → −∞ Boundary one pt out state: t → ∞ � � � � � � v 1 � � v 1 � � � � � � � � � � � � � � � � � � � � � � � �

Integrable boundary field theory: Bootstrap Boundary one particle in state: t → −∞ Boundary one pt out state: t → ∞ � � � � �� �� � � �� �� v 1 � � v 1 �� �� � � �� �� � � �� �� � � �� �� � � �� �� θ � � �� �� � � �� �� �� �� � � � � �� �� �� �� � � � � � � � �

Integrable boundary field theory: Bootstrap Boundary one particle in state: t → −∞ Boundary one pt out state: t → ∞ � � � � �� �� � � �� �� v 1 � � v 1 �� �� � � �� �� � � �� �� � � �� �� � � �� �� θ � � �� �� � � �� �� �� �� � � � � �� �� �� �� � � � � � � � � Free in particle Free out particle