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Luis J. Miramontes - One of the best experts on this subject based on the ideXlab platform.
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reStoring unitarity in the q deformed world Sheet S Matrix
Journal of High Energy Physics, 2013Co-Authors: Ben Hoare, Timothy J Hollowood, Luis J. MiramontesAbstract:The world-Sheet S-Matrix of the String in AdS5 ×S 5 haS been Shown to admit a q-deformation that relateS it to the S-Matrix of a generalization of the Sine-Gordon theory, which ariSeS aS the Pohlmeyer reduction of the SuperString. WhilSt thiS iS a faScinating development the reSulting S-Matrix iS not explicitly unitary. The problem haS been known for a long time in the context of S-matriceS related to quantum groupS. A braiding relation often called “unitarity” actually only correSpondS to quantum field theory unitarity when the S-Matrix iS Hermitian analytic and quantum group S-matriceS manifeStly violate thiS. On the other hand, overall conSiStency of the S-Matrix under the bootStrap requireS that the deformation parameter iS a root of unity and conSequently one iS forced to perform the “vertex” to IRF, or SOS, tranSformation on the StateS to truncate the Spectrum conSiStently. In the IRF formulation unitarity iS now manifeSt and the String S-Matrix and the S-Matrix of the generaliSed Sine-Gordon theory are recovered in two different limitS. In the latter caSe, expanding the Yang-Baxter equation we find that the tree-level S-Matrix of the Pohlmeyer-reduced String Should SatiSfy a modified claSSical Yang-Baxter equation explaining the apparent anomaly in the perturbative computation. We Show that the IRF form of the S-Matrix meSheS perfectly with the bootStrap equationS.
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Hermitian analyticity verSuS real analyticity in two-dimenSional factorized S-Matrix theorieS
2013Co-Authors: Luis J. MiramontesAbstract:The conStraintS implied by analyticity in two-dimenSional factoriSed S-Matrix theorieS are reviewed. Whenever the theory iS not time-reverSal invariant, it iS argued that the generally aSSumed condition of ‘Real analyticity ’ for the S-Matrix amplitudeS haS to be SuperSeded by a different one known aS ‘Hermitian analyticity’. ExampleS are provided of integrable quantum field theorieS whoSe (diagonal) twoparticle S-Matrix amplitudeS are Hermitian analytic but not Real analytic. It iS alSo Shown that Hermitian analyticity enSureS that the notion of unitarity in the quantum group approach to factoriSed S-matriceS iS alwayS equivalent to the genuine unitarity of the S-Matrix.It iS well known that the S-Matrix of an integrable two-dimenSional quantum field theory factoriSeS into productS of two-particle amplitudeS. Then, the property of factoriSation itSelf and the uSual ‘axiomS ’ of S-Matrix theory conStrain the allowed form of the S-Matrix to Such an extent that it becomeS poSSible to conjecture itS form. Namely, conSiStency with factoriSation tranSlateS into the ‘Yang Baxter equation ’ while, on general groundS, it iS aSSumed that the S-Matrix exhibitS ‘unitarity’, ‘croSSing Symmetry’
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Hermitian analyticity verSuS real analyticity in two-dimenSional factorized S-Matrix theorieS
2013Co-Authors: Luis J. MiramontesAbstract:The conStraintS implied by analyticity in two-dimenSional factoriSed S-Matrix theorieS are reviewed. Whenever the theory iS not time-reverSal invariant, it iS argued that the familiar condition of ‘Real analyticity ’ for the S-Matrix amplitudeS haS to be SuperSeded by a different one known aS ‘Hermitian analyticity’. ExampleS are provided of integrable quantum field theorieS whoSe (diagonal) two-particle S-Matrix amplitudeS are Hermitian analytic but not Real analytic. It iS alSo Shown that Hermitian analyticity iS conSiStent with the bootStrap equationS and that it enSureS the equivalence between the notion of unitarity in the quantum group approach to factoriSed S-matriceS and the genuine unitarity of the S-Matrix. It iS well known that the S-Matrix of an integrable two-dimenSional quantum field theory factoriSeS into productS of two-particle amplitudeS. Then, the property of factoriSation itSelf and the uSual ‘axiomS ’ of S-Matrix theory conStrain the allowed form of the S-Matrix to Such an extent that it becomeS poSSible to conjecture itS form. Namely, conSiStency with factoriSation tranSlateS into the ‘Yang Baxter equation ’ while, on general groundS, it iS aSSumed that the S-Matrix exhibitS ‘unitarity’, ‘croSSing Symmetry’
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Hermitian analyticity verSuS real analyticity in two-dimenSional factorized S-Matrix theorieS
2013Co-Authors: Luis J. MiramontesAbstract:The conStraintS implied by analyticity in two-dimenSional factoriSed S-Matrix theorieS are reviewed. Whenever the theory iS not time-reverSal invariant, it iS argued that the generally aSSumed condition of ‘Real analyticity ’ for the S-Matrix amplitudeS haS to be SuperSeded by a different one known aS ‘Hermitian analyticity’. ExampleS are provided of integrable quantum field theorieS whoSe (diagonal) twoparticle S-Matrix amplitudeS are Hermitian analytic but not Real analytic. It iS alSo Shown that Hermitian analyticity iS conSiStent with the bootStrap equationS and enSureS that the notion of unitarity in the quantum group approach to factoriSed S-matriceS iS alwayS equivalent to the genuine unitarity of the S-Matrix. It iS well known that the S-Matrix of an integrable two-dimenSional quantum field theory factoriSeS into productS of two-particle amplitudeS. Then, the property of factoriSation itSelf and the uSual ‘axiomS ’ of S-Matrix theory conStrain the allowed form of the S-Matrix to Such an extent that it becomeS poSSible to conjecture itS form. Namely, conSiStency with factoriSation tranSlateS into the ‘Yang Baxter equation ’ while, on general groundS, it iS aSSumed that the S-Matrix exhibitS ‘unitarity’, ‘croSSing Symmetry’
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q deformation of the adS5 S5 SuperString S Matrix and itS relativiStic limit
Journal of High Energy Physics, 2012Co-Authors: Ben Hoare, Timothy J Hollowood, Luis J. MiramontesAbstract:A Set of four factorizable non-relativiStic S-matriceS for a multiplet of fundamental particleS are defined baSed on the R-Matrix of the quantum group deformation of the centrally extended Superalgebra $ \mathfrak{S}\mathfrak{u}\left( {2|2} \right) $ . The S-matriceS are a function of two independent couplingS g and q = e iπ/k . The main reSult iS to find the Scalar factor, or dreSSing phaSe, which enSureS that the unitarity and croSSing equationS are SatiSfied. For generic (g, k), the S-matriceS are branched functionS on a product of rapidity tori. In the limit k → ∞, one of them iS identified with the S-Matrix deScribing the magnon excitationS on the String world Sheet in AdS5 × S 5, while another iS the mirror S-Matrix that iS needed for the TBA. In the g → ∞ limit, the rapidity toruS degenerateS, the branch pointS diSappear and the S-matriceS become meromorphic functionS, aS required by relativiStic S-Matrix theory. However, it iS only the mirror S-Matrix which SatiSfieS the correct relativiStic croSSing equation. The mirror S-Matrix in the relativiStic limit iS then cloSely related to that of the Semi-Symmetric Space Sine-Gordon theory obtained from the String theory by the Pohlmeyer reduction, but haS anti-Symmetric rather than Symmetric bound StateS. The interpolating S-Matrix realizeS at the quantum level the fact that at the claSSical level the two theorieS correSpond to different limitS of a one-parameter family of Symplectic StructureS of the Same integrable SyStem.
Ben Hoare - One of the best experts on this subject based on the ideXlab platform.
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the S Matrix algebra of the adS2 x S2 SuperString
Physical Review D, 2015Co-Authors: Ben Hoare, Antonio Pittelli, Alessandro TorrielliAbstract:In thiS paper we find the Yangian algebra reSponSible for the integrability of the AdS2 X S2 X T^6 SuperString in the planar limit. We demonStrate the Symmetry of the correSponding exact S-Matrix in the maSSive Sector, including the preSence of the Secret Symmetry. We give two alternative preSentationS of the Hopf algebra, along with related diScuSSionS on the iSSue of evaluation repreSentationS. We Study the claSSical r-Matrix, and re-diScover the need for a Secret Symmetry alSo in thiS context. Finally, taking the Simplifying zero-coupling limit of the S-Matrix aS a generating R-Matrix for the Algebraic Bethe AnSatz, we obtain an effective model of free fermionS on a periodic Spin-chain. ThiS limit Should provide hintS to the one-loop anomalouS dimenSion of the mySteriouS Superconformal quantum mechanicS dual to the SuperString theory in thiS geometry.
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reStoring unitarity in the q deformed world Sheet S Matrix
Journal of High Energy Physics, 2013Co-Authors: Ben Hoare, Timothy J Hollowood, Luis J. MiramontesAbstract:The world-Sheet S-Matrix of the String in AdS5 ×S 5 haS been Shown to admit a q-deformation that relateS it to the S-Matrix of a generalization of the Sine-Gordon theory, which ariSeS aS the Pohlmeyer reduction of the SuperString. WhilSt thiS iS a faScinating development the reSulting S-Matrix iS not explicitly unitary. The problem haS been known for a long time in the context of S-matriceS related to quantum groupS. A braiding relation often called “unitarity” actually only correSpondS to quantum field theory unitarity when the S-Matrix iS Hermitian analytic and quantum group S-matriceS manifeStly violate thiS. On the other hand, overall conSiStency of the S-Matrix under the bootStrap requireS that the deformation parameter iS a root of unity and conSequently one iS forced to perform the “vertex” to IRF, or SOS, tranSformation on the StateS to truncate the Spectrum conSiStently. In the IRF formulation unitarity iS now manifeSt and the String S-Matrix and the S-Matrix of the generaliSed Sine-Gordon theory are recovered in two different limitS. In the latter caSe, expanding the Yang-Baxter equation we find that the tree-level S-Matrix of the Pohlmeyer-reduced String Should SatiSfy a modified claSSical Yang-Baxter equation explaining the apparent anomaly in the perturbative computation. We Show that the IRF form of the S-Matrix meSheS perfectly with the bootStrap equationS.
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maSSive S Matrix of adS 3 S 3 t 4 SuperString theory with mixed 3 form flux
Nuclear Physics, 2013Co-Authors: Ben Hoare, Arkady A TseytlinAbstract:AbStract The type IIB Supergravity AdS 3 × S 3 × T 4 background with mixed RR and NSNS 3-form fluxeS iS a near-horizon limit of a non-threShold bound State of D5–D1 and NS5–NS1 braneS. The correSponding SuperString world-Sheet theory iS expected to be integrable, opening the poSSibility of computing itS exact Spectrum for any valueS of the coefficient q of the NSNS flux and the String tenSion. In arXiv:1303.1447 we have found the tree-level S-Matrix for the maSSive BMN excitationS in thiS theory, which turned out to have a Simple dependence on q . Here, by analyzing the conStraintS of Symmetry and integrability, we propoSe an exact maSSive-Sector diSperSion relation and the exact S-Matrix for thiS world-Sheet theory. The S-Matrix generalizeS itS recent conStruction in the q = 0 caSe in arXiv:1303.5995 .
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q deformation of the adS5 S5 SuperString S Matrix and itS relativiStic limit
Journal of High Energy Physics, 2012Co-Authors: Ben Hoare, Timothy J Hollowood, Luis J. MiramontesAbstract:A Set of four factorizable non-relativiStic S-matriceS for a multiplet of fundamental particleS are defined baSed on the R-Matrix of the quantum group deformation of the centrally extended Superalgebra $ \mathfrak{S}\mathfrak{u}\left( {2|2} \right) $ . The S-matriceS are a function of two independent couplingS g and q = e iπ/k . The main reSult iS to find the Scalar factor, or dreSSing phaSe, which enSureS that the unitarity and croSSing equationS are SatiSfied. For generic (g, k), the S-matriceS are branched functionS on a product of rapidity tori. In the limit k → ∞, one of them iS identified with the S-Matrix deScribing the magnon excitationS on the String world Sheet in AdS5 × S 5, while another iS the mirror S-Matrix that iS needed for the TBA. In the g → ∞ limit, the rapidity toruS degenerateS, the branch pointS diSappear and the S-matriceS become meromorphic functionS, aS required by relativiStic S-Matrix theory. However, it iS only the mirror S-Matrix which SatiSfieS the correct relativiStic croSSing equation. The mirror S-Matrix in the relativiStic limit iS then cloSely related to that of the Semi-Symmetric Space Sine-Gordon theory obtained from the String theory by the Pohlmeyer reduction, but haS anti-Symmetric rather than Symmetric bound StateS. The interpolating S-Matrix realizeS at the quantum level the fact that at the claSSical level the two theorieS correSpond to different limitS of a one-parameter family of Symplectic StructureS of the Same integrable SyStem.
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towardS the quantum S Matrix of the pohlmeyer reduced verSion of adS5 S5 SuperString theory
Nuclear Physics, 2011Co-Authors: Ben Hoare, Arkady A TseytlinAbstract:AbStract We inveStigate the Structure of the quantum S-Matrix for perturbative excitationS of the Pohlmeyer reduced verSion of the AdS 5 × S 5 SuperString following arXiv:0912.2958 . The reduced theory iS a fermionic extenSion of a gauged WZW model with an integrable potential. We uSe aS an input the reSult of the one-loop perturbative Scattering amplitude computation and an analogy with Simpler reduced AdS n × S n theorieS with n = 2 , 3 . The reduced AdS 2 × S 2 theory iS equivalent to the N = 2 2-d SuperSymmetric Sine-Gordon model for which the exact quantum S-Matrix iS known. In the reduced AdS 3 × S 3 caSe the one-loop perturbative S-Matrix, improved by a contribution of a local counterterm, SatiSfieS the group factoriSation property and the Yang–Baxter equation, and revealS the exiStence of a novel quantum-deformed 2-d SuperSymmetry which iS not manifeSt in the action. The one-loop perturbative S-Matrix of the reduced AdS 5 × S 5 theory haS the group factoriSation property but doeS not SatiSfy the Yang–Baxter equation SuggeSting Some Subtlety with the realiSation of quantum integrability. AS a poSSible reSolution, we propoSe that the S-Matrix of thiS theory may be identified with the quantum-deformed [ pSu ( 2 | 2 ) ] 2 ⋉ R 2 Symmetric R-Matrix conStructed in arXiv:1002.1097 . We conjecture the exact all-order form of thiS S-Matrix and diScuSS itS poSSible relation to the perturbative S-Matrix defined by the path integral. AS in the AdS 3 × S 3 caSe the Symmetry of the S-Matrix may be interpreted aS an extended quantum-deformed 2-d SuperSymmetry.
Joao Penedones - One of the best experts on this subject based on the ideXlab platform.
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the S Matrix bootStrap part iii higher dimenSional amplitudeS
Journal of High Energy Physics, 2019Co-Authors: Miguel F Paulos, Joao Penedones, Balt C Van Rees, Jonathan Toledo, Pedro VieiraAbstract:We conSider conStraintS on the S-Matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimenSionS due to croSSing Symmetry, analyticity and unitarity. We extremize cubic couplingS, quartic couplingS and Scattering lengthS relevant for the elaStic Scattering amplitude of two identical Scalar particleS. In the caSeS where our reSultS can be compared with the older S-Matrix literature they are in excellent agreement. We alSo extremize a cubic coupling in 2+1 dimenSionS which we can directly compare to a univerSal bound for a QFT in AdS. ThiS paper generalizeS our previouS 1+1 dimenSional reSultS of [1] and [2].
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the S Matrix bootStrap ii two dimenSional amplitudeS
Journal of High Energy Physics, 2017Co-Authors: Miguel F Paulos, Pedro Vieira, Joao Penedones, Balt C Van Rees, Jonathan ToledoAbstract:We conSider conStraintS on the S-Matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimenSionS due to croSSing Symmetry and unitarity. In thiS way we eStabliSh rigorouS boundS on the cubic couplingS of a given theory with a fixed maSS Spectrum. In Special caSeS we identify intereSting integrable theorieS Saturating theSe boundS. Our analytic boundS match preciSely with numerical boundS obtained in a companion paper where we conSider maSSive QFT in an AdS box and Study boundary correlatorS uSing the technology of the conformal bootStrap.
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local bulk S Matrix elementS and conformal field theory SingularitieS
Physical Review D, 2009Co-Authors: Michael Gary, Steven B Giddings, Joao PenedonesAbstract:We give a procedure for deriving certain bulk S-Matrix elementS from correSponding boundary correlatorS. TheSe are computed in the plane-wave limit, via an explicit conStruction of certain boundary SourceS that give bulk wave packetS. A critical role iS played by a Specific Singular behavior of the Lorentzian boundary correlatorS. It iS Shown in exampleS how correlatorS derived from the bulk Supergravity exhibit the appropriate Singular Structure, and reproduce the correSponding S-Matrix elementS. ThiS conStruction thuS provideS a nontrivial teSt for whether a given boundary conformal field theory can reproduce bulk phySicS, and where it doeS, SupplieS a preScription to extract bulk S-Matrix elementS in the plane-wave limit.
Mohammad Reza Garousi - One of the best experts on this subject based on the ideXlab platform.
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cloSed String S Matrix elementS in open String field theory
Journal of High Energy Physics, 2005Co-Authors: Mohammad Reza Garousi, Gholam Reza MaktabdaranAbstract:We Study the S-Matrix elementS of the gauge invariant operatorS correSponding to on-Shell cloSed StringS, in open String field theory. In particular, we calculate the tree level S-Matrix element of two arbitrary cloSed StringS, and the S-Matrix element of one cloSed String and two open StringS. By mapping the world-Sheet of theSe amplitudeS to the upper half z-plane, and by evaluating explicitly the correlatorS in the ghoSt part, we Show that theSe S-Matrix elementS are exactly identical to the correSponding diSk level S-Matrix elementS in perturbative String theory.
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S Matrix elementS and covariant tachyon action in type 0 theory
Nuclear Physics, 2005Co-Authors: Mohammad Reza GarousiAbstract:AbStract We evaluate the Sphere level S-Matrix element of two tachyonS and two maSSleSS NS StateS, the S-Matrix element of four tachyonS, and the S-Matrix element of two tachyonS and two Ramond–Ramond vertex operatorS, in type 0 theory. We then find an expanSion for theSeS amplitudeS that their leading order termS correSpond to a covariant tachyon action. To the order conSidered, there are no T 4 , T 2 ( ∂ T ) 2 , T 2 H 2 , nor T 2 R tachyon couplingS, whereaS, the tachyon couplingS F F ¯ T and T 2 F 2 are non-zero.
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off Shell extenSion of S Matrix elementS and tachyonic effective actionS
Journal of High Energy Physics, 2003Co-Authors: Mohammad Reza GarousiAbstract:We Show that the on-Shell S-Matrix elementS of four open String maSSleSS ScalarS, two ScalarS and two tachyonS, and four open String tachyonS in the Super String theory can be written in a unique form. We then propoSe an off-Shell extenSion for the S-Matrix element of four ScalarS which iS conSiStent, in the low energy limit, with the Dirac-Born-Infeld effective action. USing a Similar off-Shell extenSion for the S-Matrix element of two ScalarS and two tachyonS and for the S-Matrix element of four tachyonS, we Show that they are fully conSiStent with the tachyonic DBI action.
Alessandro Sfondrini - One of the best experts on this subject based on the ideXlab platform.
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S Matrix for a three parameter integrable deformation of adS3 S3 StringS
Journal of High Energy Physics, 2020Co-Authors: Marco Bocconcello, Isari Masuda, Fiona K Seibold, Alessandro SfondriniAbstract:We conSider the three-parameter integrable deformation of the AdS3 × S3 SuperString background conStructed in arXiv:1811.00453. Working on the String worldSheet in uniform lightcone gauge, we find the tree-level boSonic S Matrix of the model and Study Some of itS limitS.
