# Course News

Dear all,

handwritten, draft notes for lecture #1 of Caprini's course 'Gravitational waves' are online.

The organizers

The fifth and last IPhT course of this academic year will start on Friday, June 3rd, with the first of a series of five lectures by Chiara Caprini on Gravitational waves. For the abstract and further details, see the course's web page.

The lectures are open to all: students, postdocs and researchers, whether IPhT members or outsiders. Do not hesitate to recommend them to anyone who might be interested.

We are looking for volunteers who would type lecture notes under the supervision of the speaker. Please contact the organizers (or the speaker) if you are interested.

Summary of second Volin's lecture 'Quantum integrability: old and new tools' (tomorrow Friday May 20th at 10:00). Knowledge of the material from the previous lecture is desirable but not compulsory.

Part IA: Notion of a quantum spectral curve (QSC) is introduced and it is explained in what sense it is a quantisation of a classical curve. Discussion includes the historically first example: relation between Schrodinger and Hamilton-Jacobi equations. On the next step, we introduce a geometric description of QSC for systems with GL(N) symmetry as a special-type section of a holomorphic bundle with fiber being the maximal flag of C^N. This construction naturally arises whenever we solve order-N differential or finite-difference equations. Symmetries behind the geometric constructions are discussed.

Part IB: We discuss the ring of supersymmetric polynomials and demonstrate its isomorphism to the ring of symmetric polynomials, in the case N=infty, M=infty (superduality). Inspired by these observation, we translate these ideas to relation between GL(N|M) and GL(N+M) QSC's thus effectively formulating QSC for GL(N|M) case. Part I is finalised by a practical example: new efficient way to solve Bethe equations for rational spin chains (including the Heisenberg XXX).

Part IIA (After coffee break): Baxter equation has two solutions. We discuss the role of the dominant and subdominant solutions for the case of compact SU(2) and non-compact SL(2) spin chains. Non-compact case is rich with Stoke's phenomena; it also brings us the need to perform Borel re-summation, prescription for the latter naturally introduces the notion of QSC analytic in the upper or lower half-planes.

Part IIB: We motivate and formulate QSC that encodes the spectrum of planar N=4 SYM.

Dear all, please find below a short summary of the first Volin's lecture, to be held tomorrow at 10:00 in IPhT.

The Organizers

Part 1 (before coffee break):

Bethe equations for the spectrum of anharmonic oscillator.

We will depart from the Schrodinger equation with polynomial potential,

discuss WKB approximation, Stokes phenomena, and derive the Bohr-Sommerfeld

quantization condition using very basic analytic continuation arguments.

Then we discuss the full quantum picture and show that the spectral

determinants for this system obey certain Wronskian relations which lead to

Bethe equations on the Hamiltonian's eigenvalues.

Part 2 (after coffee break)

Characters and integrability

We will recall some basic facts about Schur-Weyl duality and character

formulae. Then the discussion of SU(N) XXX spin chain from this perspective

is due, with the goal to introduce the concept of transfer matrices and

Hirota equations. We end up with presenting Wronskian solution of the

Hirota equations and Wronskian relations on Baxter Q-functions which, for

the SU(2) case, happen to be identical to those we observed when solving

the anharmonic oscillator.

Time permitting, generalization to non-compact supersymmetric cases will be

given, otherwise it is the first topic of the lecture next week.

Dear all,

The second part of the course 'Quantum integrability: old and new tools', held by Dmytro Volin, will start on next Friday, 13th May at 10:00AM.

Dmytro proposes to give 1-2 supplementary exercise sessions: we will discuss this possibility Friday.

The organizers

PS Draft notes for Serban's lectures are available here:

https://www.ipht.fr/Docspht//search/article.php?id=t16/026

Dear all,

(draft) notes including the second lecture of the course "Integrability: old and new tools", written by D. Serban, are available online:

https://www.ipht.fr/Docspht//search/article.php?id=t16/026

See you tomorrow for the third lecture.

The organizers

Dear all,

(draft) notes on the first lecture of the course "Integrability: old and new tools", written by D. Serban, are available online:

https://www.ipht.fr/Docspht//search/article.php?id=t16/026

the organizers

The fourth IPhT course of this academic year will start on Friday, April 1st, with the first of a series of six lectures by Didina Serban and Dmytro Volin on 'Quantum integrability: old and new tools'. For more details, see the course's web page:

https://courses.ipht.fr/?q=en/node/18

The lectures are open to all: students, postdocs, and researchers, whether IPhT members or outsiders. Do not hesitate to recommend them to anyone who might be interested.