We study the classical spectrum of string theory on AdS 5 × S 5 in the Hofman-Maldacena limit. We find a family of classical solutions corresponding to Giant Magnons with two independent angular momenta on S 5 . These solutions are related via Pohlmeyer's reduction procedure to the charged solitons of the Complex sine-Gordon equation. The corresponding string states are dual to BPS boundstates of many magnons in the spin-chain description of planar N = 4 SUSY Yang-Mills.The exact dispersion relation for these states is obtained from a purely classical calculation in string theory.

We study the conjectured exact S-matrix for the scattering of BPS magnon boundstates in the spin-chain description of planar N = 4 SUSY Yang-Mills. The conjectured S-matrix exhibits both simple and double poles at complex momenta. Some of these poles lie parametrically close to the real axis in momentum space on the branch where particle energies are positive. We show that all such poles are precisely accounted for by physical processes involving one or more on-shell intermediate particles belonging to the known BPS spectrum.

We study a family of classical string solutions with large spins on R t S 3 subspace of AdS 5 S 5 background, which are related to Complex sine-Gordon solitons via Pohlmeyer's reduction. The equations of motion for the classical strings are cast into Lamé equations and Complex sine-Gordon equations. We solve them under periodic boundary conditions, and obtain analytic profiles for the closed strings. They interpolate two kinds of known rigid configurations with two spins: on one hand, they reduce to folded or circular spinning/rotating strings in the limit where a soliton velocity goes to zero, while on the other hand, the dyonic giant magnons are reproduced in the limit where the period of a kink-array goes to infinity.

We study the scattering of magnon boundstates in the spin-chain description of planar N = 4 SUSY Yang-Mills. Starting from the conjectured exact S-matrix for magnons in the SU (2) sector, we calculate the corresponding S-matrix for boundstates with an arbitrary number of constituent magnons. The resulting expression has an interesting analytic structure with both simple and double poles. We also calculate the semiclassical S-matrix for the scattering of the corresponding excitations on the string worldsheet known as Dyonic Giant Magnons. We find precise agreement with the magnon boundstate S-matrix in the limit of large 't Hooft coupling.

Addressing many of the world's contemporary challenges requires a multifaceted and integrated approach, and interdisciplinary research (IDR) has become increasingly central to both academic interest and government science policies. Although higher interdisciplinarity is then often assumed to be associated with higher research impact, there has been little solid scientific evidence supporting this assumption. Here, we provide verifiable evidence that interdisciplinarity is statistically significantly and positively associated with research impact by focusing on highly cited paper clusters known as the research fronts (RFs). Interdisciplinarity is uniquely operationalised as the effective number of distinct disciplines involved in the RF, computed from the relative abundance of disciplines and the affinity between disciplines, where all natural sciences are classified into eight disciplines. The result of a multiple regression analysis (n = 2,560) showed that an increase by one in the effective number of disciplines was associated with an approximately 20% increase in the research impact, which was defined as a field-normalised citation-based measure. A new visualisation technique was then applied to identify the research areas in which high-impact IDR is underway and to investigate its evolution over time and across disciplines. Collectively, this work establishes a new framework for understanding the nature and dynamism of IDR in relation to existing disciplines and its relevance to science policymaking.

In this paper we discuss the asymptotic spectrum of the spin chain description of planar N = 4 SUSY Yang-Mills. The states appearing in the spectrum belong to irreducible representations of the unbroken supersymmetry SU (2|2) × SU (2|2) with non-trivial extra central extensions. The elementary magnon corresponds to the bifundamental representation while boundstates of Q magnons form a certain short representation of dimension 16Q 2 . Generalising the Beisert's analysis of the Q = 1 case, we derive the exact dispersion relation for these states by purely group theoretic means.

We study a family of classical strings on R × S 3 subspace of the AdS 5 × S 5 background that interpolates between pulsating strings and single-spike strings. They are obtained from the helical strings of hep-th/0609026 by interchanging worldsheet time and space coordinates, which maps rotating/spinning string states with large spins to oscillating states with large winding numbers. From a finite-gap perspective, this transformation is realised as an interchange of quasi-momentum and quasi-energy defined for the algebraic curve. The gauge theory duals are also discussed, and are identified with operators in the non-holomorphic sector of N = 4 super Yang-Mills. They can be viewed as excited states above the "antiferromagnetic" state, which is "the farthest from BPS" in the spin-chain spectrum. Furthermore, we investigate helical strings on AdS 3 × S 1 in an appendix.

We consider open spinning string solutions on an AdS 4 ×S 2 -brane (D5-brane) in the bulk AdS 5 × S 5 background. By taking account of the breaking of SO(6) R to SO(3) H × SO(3) V due to the presence of the AdS-brane, the open rotating string ansatz is discussed. We construct the elliptic folded/circular open string solutions in the SU (2) and the SL(2) sectors, so that they satisfy the appropriate boundary conditions. On the other hand, in the SU (2) sector of the gauge theory, we compute the matrix of anomalous dimension of the defect operator, which turns out to be the Hamiltonian of an open integrable spin chain. Then we consider the coordinate Bethe ansatz with arbitrary number of impurities, and compare the boundary condition of the Bethe wavefunction with that of the corresponding open string solution. We also discuss the Bethe ansatz for the open SL(2) spin chain with several supports from the string theory side. Then, in both SU (2) and SL(2) sectors, we analyze the Bethe equations in the thermodynamic limit and formulate the 'doubling trick' on the Riemann surface associated with the gauge theory.10 The one-loop correction to the energy of closed spinning strings in the SU (2) and the SL(2) sectors are calculated in [59] and [60] respectively.