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SUMMARY:Dmytro Volin (Nordita)
DTSTART;VALUE=DATE-TIME:20200507T090000Z
DTEND;VALUE=DATE-TIME:20200507T110000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/1
DESCRIPTION:Title: Completeness of Bethe equations\nby Dmytro Volin (Nordi
ta) as part of London Integrability Journal Club\n\n\nAbstract\nWe review
a proof of bijection between eigenstates of the Bethe algebra and solution
s of Bethe equations written as a Wronskian quantisation condition or as Q
Q-relations on Young diagrams. Furthermore\, it is demonstrated that the B
ethe algebra is maximal commutative and it has simple spectrum every time
it is diagonalisable. The proof covers rational gl(m|n) spin chains in th
e defining representation with the famous Heisenberg spin chain being a pa
rticular subcase. The proof is rigorous (no general position arguments ar
e used). We do not rely on the string hypothesis and moreover we conjectur
e a precise meaning of Bethe strings as a consequence of the proposed proo
f.\nA short introduction with necessary facts about polynomial rings will
be given at the beginning of the talk. \nBased on 2004.02865\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shota Komatsu (IAS)
DTSTART;VALUE=DATE-TIME:20200515T130000Z
DTEND;VALUE=DATE-TIME:20200515T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/2
DESCRIPTION:Title: Wilson loops as matrix product states\nby Shota Komatsu
(IAS) as part of London Integrability Journal Club\n\n\nAbstract\nIn his
paper in 1979\, Polyakov envisaged a possibility of reformulating the gaug
e theory as a Principal Chiral Model defined on a space of loops and discu
ssed "the loop-space integrability". This idea\, together with a closely r
elated idea of the loop equation\, led to numerous important results in ma
trix models and 2d gauge theories\, but its application to four-dimensiona
l gauge theories had only limited success. Now\, after 50 years\, we have
a concrete example of integrable four-dimensional gauge theory\, N=4 SYM.
However integrability in N=4 SYM is formulated mostly in terms of local op
erators\, although important progress has been made in constructing the Ya
ngian for the Wilson loops. In this talk\, I will present a framework whic
h would bridge these two distant notions of integrabililty. The key player
in the story is a correlation function of a local operator and the Wilson
loop. I reformulate the gauge-theory computation of this observable as an
overlap between an energy eigenstate of a spin chain and a matrix product
state (MPS). Unlike standard MPS's discussed in the literature\, our MPS
has infinite bond dimensions in order to accommodate infinite dimensionali
ty of the space of loops. It provides an "intertwiner" between integrable
structures of the local operators and the Wilson loops\, and in particular
implies the existence of a special set of deformations of the Wilson loop
which satisfy the QQ-relation. I will also explain how to formulate a non
perturbative bootstrap program based on the results obtained in this frame
work and compute the correlator of the circular BPS Wilson loop and genera
l non-BPS operators at finite coupling\, emphasizing the relation to and t
he difference from other observables that were computed by a similar appro
ach.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ines Aniceto (Southampton U)
DTSTART;VALUE=DATE-TIME:20200521T130000Z
DTEND;VALUE=DATE-TIME:20200521T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/3
DESCRIPTION:Title: Integrable Field Theories with an Interacting Massless
Sector\nby Ines Aniceto (Southampton U) as part of London Integrability Jo
urnal Club\n\n\nAbstract\nIntegrability techniques have played a major rol
e in the study the AdS/CFT correspondence\, providing an accurate descript
ion of different string theoretic observables beyond the weak or strong c
oupling perturbation theory. However\, the case of string on certain $AdS_
3$ backgrounds provided new challenges in the form of massless excitations
. Difficulties in incorporating these into the integrable description have
led to disagreements concerning the energy of massive physical states. \n
In general integrable theories\, massless and massive sectors can generall
y be treated separately. We know this cannot be the case in $AdS_3$\, but
a full TBA description of the interaction between the sectors is yet to be
found. Surprisingly\, such a description can found in a family of integra
ble field theories — homogeneous sine-Gordon models. Here\, one can tak
e a double scaling limit of the adjustable parameters and zoom into a regi
me described by a TBA where the massless sector does not decouple and cont
ributes to the energy of massive particles at the same order as for which
the Bethe ansatz would suffice in a massive theory.\n\nannouncements also
on https://integrability-london.weebly.com/\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamas Gombor (Wigner Research Centre for Physics)
DTSTART;VALUE=DATE-TIME:20200528T130000Z
DTEND;VALUE=DATE-TIME:20200528T150000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/4
DESCRIPTION:Title: Boundary states\, overlaps\, nesting and bootstrapping
AdS/dCFT\nby Tamas Gombor (Wigner Research Centre for Physics) as part of
London Integrability Journal Club\n\n\nAbstract\nRecently there have been
renewed interest and relevant progress in calculating overlaps between per
iodic multiparticle states and integrable boundary states. They appear in
quite distinct parts of theoretical physics including statistical physics
and the gauge/string duality.\nI will give a summary of known overlap for
mulas and analyze the connection between selection rules and symmetries. I
will introduce a nesting procedure for boundary states which provides the
factorizing overlaps for higher rank algebras automatically. This method
can be used for the calculation of the asymptotic all-loop 1-point functio
ns in AdS/dCFT. In doing so I will present the solutions of the YBE for th
e K-matrices with centrally extended su(2|2) symmetry and the generic over
laps of the corresponding boundary states.\nBased on 2004.11329\n
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BEGIN:VEVENT
SUMMARY:Olof Ohlsson Sax (Nordita)
DTSTART;VALUE=DATE-TIME:20200604T140000Z
DTEND;VALUE=DATE-TIME:20200604T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/5
DESCRIPTION:Title: Crossing equations for mixed flux AdS3/CFT2\nby Olof Oh
lsson Sax (Nordita) as part of London Integrability Journal Club\n\n\nAbst
ract\nI will give an overview of recent progress in understanding string t
heory in AdS3 backgrounds with a mixture of\nRamond-Ramond and Neveu-Schwa
rz-Neveu-Schwarz three-form flux. Such theories are integrable\, but provi
de many features\nnot encountered in the more familiar case of pure Ramond
-Ramond flux. In this talk I will explore the analytic structure\nof the d
ispersion relation of the world-sheet excitations and how it relates to th
e crossing equations of the\ntwo-particle S matrix. Determining the dressi
ng phases of the mixed flux S matrix is the next major step in using\ninte
grability to the AdS3/CFT2 correspondence.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gwenael Ferrando (Ecole Normale Superieure)
DTSTART;VALUE=DATE-TIME:20200611T140000Z
DTEND;VALUE=DATE-TIME:20200611T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/6
DESCRIPTION:Title: Fishnet CFT: TBA and Non-compact Spin Chain\nby Gwenael
Ferrando (Ecole Normale Superieure) as part of London Integrability Journ
al Club\n\n\nAbstract\nThe fishnet CFT is a non-unitary CFT of two matrix
complex scalar fields interacting via a single quartic potential. The chir
al nature of the interaction strongly constrains the Feynman diagrams aris
ing at each order in perturbation theory\, those that survive are of fishn
et type. In this talk\, I will present the TBA equations for the conformal
dimensions of multi-magnon local operators in this theory. I will emphasi
ze the need to diagonalize suitable graph-building operators in order to d
etermine the asymptotic data\, dispersion relation and S matrix\, on which
the TBA relies. A dual version of the TBA equations\, relating D-dimensio
nal graphs to two-dimensional sigma models\, will also be examined. The la
st part of the talk will be devoted to the presentation of the underlying
non-compact spin chain and of additional results regarding diagonalization
of graph-building operators.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlo Meneghelli (Oxford)
DTSTART;VALUE=DATE-TIME:20200723T140000Z
DTEND;VALUE=DATE-TIME:20200723T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/7
DESCRIPTION:Title: Pre-fundamental representations for the Hubbard model a
nd AdS/CFT\nby Carlo Meneghelli (Oxford) as part of London Integrability J
ournal Club\n\n\nAbstract\nThere is a class of representations of quantum
groups\, referred to as prefundamental representations\, that plays an imp
ortant role in the solution of integrable models. The first example of suc
h representations was given by V. Bazhanov\, S. Lukyanov and A. Zamolodchi
kov in the context of two dimensional conformal field theory in order to c
onstruct Baxter Q-operators as transfer matrices. At the same time\, there
is a rather exceptional quantum group that governs the integrable structu
re of the one dimensional Hubbard model and plays a fundamental role in th
e AdS/CFT correspondence. In this talk I will introduce prefundamental rep
resentations for this quantum group\, explain their basic properties and d
iscuss some of their applications.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joao Caetano (YITP)
DTSTART;VALUE=DATE-TIME:20200625T140000Z
DTEND;VALUE=DATE-TIME:20200625T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/8
DESCRIPTION:Title: Exact g-functions\nby Joao Caetano (YITP) as part of Lo
ndon Integrability Journal Club\n\n\nAbstract\nThe g-function is a meas
ure of degrees of freedom associated to a boundary of two-dimensional quan
tum field theories. In integrable theories\, it can be computed exactly in
a form of the Fredholm determinant\, but it is often hard to evaluate num
erically. In this paper\, we derive functional equations---or equivalently
integral equations of the thermodynamic Bethe ansatz (TBA) type---which d
irectly compute the g-function in the simplest integrable theory\; the sin
h-Gordon theory at the self-dual point. The derivation is based on the cla
ssic result by Tracy and Widom on the relation between Fredholm determinan
ts and TBA\, which was used also in the context of topological string. As
a side result\, we present multiple integrals of Q-functions which we conj
ecture to describe a universal part of the g-function\, and discuss its im
plication to integrable spin chains.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marius de Leeuw
DTSTART;VALUE=DATE-TIME:20200709T140000Z
DTEND;VALUE=DATE-TIME:20200709T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/10
DESCRIPTION:Title: Solving the Yang-Baxter equation\nby Marius de Leeuw a
s part of London Integrability Journal Club\n\n\nAbstract\nThe Yang-Baxter
equation is an important equation that appears in many\ndifferent areas o
f physics. It signals the presence of integrable\nstructures which appear
in topics ranging from condensed matter physics\nto holography. In this ta
lk I will discuss a new method to find all\nregular solutions of the Yang-
Baxter equation by using the so-called\nboost automorphism. The main idea
behind this method is to use the\nHamiltonian rather than the R-matrix as
a starting point. I will\ndemonstrate our method by classifying all soluti
ons of the Yang-Baxter\nequation of eight-vertex type. I will also conside
r certain 9x9 and\n16x16 solutions and give new integrable models in all o
f these cases. As\na further application\, I will discuss all integrable d
eformations of\nR-matrices that appear in the lower-dimensional cases of t
he AdS/CFT\ncorrespondence.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lukyanov
DTSTART;VALUE=DATE-TIME:20200716T140000Z
DTEND;VALUE=DATE-TIME:20200716T160000Z
DTSTAMP;VALUE=DATE-TIME:20200812T042408Z
UID:LIJC/11
DESCRIPTION:Title: Density matrix for the 2D black hole from an integrable
spin chain\nby Sergei Lukyanov as part of London Integrability Journal Cl
ub\n\n\nAbstract\nTwenty years ago Maldacena\, Ooguri and Son constructed
a modular invariant partition function for the Euclidean black hole (cigar
) NLSM. They also proposed an expression for the corresponding density ma
trix.\nThis result played a key role in the formulation of the remarkable
conjecture by Ikhlef\, Jacobsen and Saleur that the Euclidean black hole N
LSM underlies the critical behaviour of a certain integrable spin chain.\n
In this talk we critically reexamine the above proposals.\n\nThe talk is b
ased on the recent (unpublished) joint work with\nV. Bazhanov and G. Kotou
sov.\n
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