Found 3 result(s)

### 07.05.2020 (Thursday)

#### Completeness of Bethe equations

Journal Club Dmytro Volin (Uppsala University)

 at: 10:00 Otherroom Zoom, instructions in abstract abstract: We review a proof of bijection between eigenstates of the Bethe algebra and solutions of Bethe equations written as a Wronskian quantisation condition or as QQ-relations on Young diagrams. Furthermore, it is demonstrated that the Bethe algebra is maximal commutative and it has simple spectrum every time it is diagonalisable. The proof covers rational gl(m|n) spin chains in the defining representation with the famous Heisenberg spin chain being a particular subcase. The proof is rigorous (no general position arguments are used). We do not rely on the string hypothesis and moreover we conjecture a precise meaning of Bethe strings as a consequence of the proposed proof. A short introduction with necessary facts about polynomial rings will be given at the beginning of the talk. Based on 2004.02865 NOTE: Part of London Integrability Journal Club. Please register at integrability-london.weebly.com to participate.

### 24.04.2013 (Wednesday)

#### Functional Bethe Ansatz for AdS/CFT integrability

Regular Seminar Dmytro Volin (Nordita)

 at: 13:15 KCLroom S4.23 abstract: Computation of conformal dimensions in planar N=4 SYM using integrability techniques was a hot topic during the last decade, with more than thousand publications devoted to it. I will tell you about our new results in this domain: Instead of the Y-system used previously, we are now able to encode the conformal dimensions, at any value of the 't Hooft coupling, in much simpler way: through a Riemann-Hilbert problem. This appears to be not only a very beautiful mathematical setup, but also the most efficient approach to explicitly compute the dimensions. For instance, we've analytically computed the so called Konishi anomalous dimension up to 8 loops in perturbation theory.

### 17.04.2013 (Wednesday)

#### Functional Bethe Ansatz for AdS/CFT spectrum

Regular Seminar Dmytro Volin (Nordita)

 at: 14:00 ICroom H503 abstract: Computation of conformal dimensions in planar N=4 SYM using integrability techniques was a hot topic during the last decade, with more than thousand publications devoted to it. I will tell you about our new results in this domain: Instead of the Y-system used previously, we are now able to encode the conformal dimensions, at any value of the 't Hooft coupling, in much simpler way: through a Riemann-Hilbert problem. This appears to be not only a very beautiful mathematical setup, but also the most efficient approach to explicitly compute the dimensions. For instance, we've analytically computed the so called Konishi anomalous dimension up to 8 loops in perturbation theory. The talk will include a pedagogical overview of the subject, no special knowledge in this domain is required.