Review of AdS/CFT Integrability, Chapter III.1: Bethe Ans?tze and the R-Matrix Formalism

The one-dimensional Heisenberg XXX spin chain appears in a special limit of the AdS/CFT integrable system. We review various ways of proving its integrability, and discuss the associated methods of solution. In particular, we outline the coordinate and the algebraic Bethe ansatz, giving reference to literature suitable for learning these techniques. Finally, we speculate which of the methods might lift to the exact solution of the AdS/CFT system, and sketch a promising method for constructing the Baxter Q-operator of the XXX chain. It allows to find the spectrum of the model using certain algebraic techniques, while entirely avoiding Bethe’s ansatz.     

Review of AdS/CFT Integrability,Chapter II.2: Quantum Strings in AdS<Subscript>5</Subscript> × S<Superscript>5</Superscript>

We review the semiclassical analysis of strings in AdS₅ × S⁵ with a focus on the relationship to the underlying integrable structures. We discuss the perturbative calculation of energies for strings with large charges, using the folded string spinning in AdS₃ ? AdS₅ as our main example. Furthermore, we review the perturbative light-cone quantisation of the string theory and the calculation of the worldsheet S-matrix.     

The Algebraic Curve of Classical Superstrings on AdS 5×S 5

We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS₅×S⁵. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar, one-loop supersymmetric gauge theory proving the complete agreement of spectra in this approximation. Membre de l'Institut Universitaire de France     

Twisted Duality Symmetry and Integrability of Hybrid Superstring on AdS2×S2

In this paper, we show that there exists a twisted duality symmetry between the Maurer-Cartan equations and the equations of motion in the hybrid formalism for the type IIB superstring in an AdS₂×S² background with Ramond-Ramond flux. As a result, from the twisted duality transformation, we construct the Lax connection with the spectral parameter, which ensures the integrability of the system.     

AdS5 (×)S1,AdS5(×)S5和AdS2(×)S2超弦模型的一种KRR参数化新方法

给出了3种典型超弦模型AdS5 (×)S1,AdS5(×)S5和AdS2(×)S2的一种简单的KRR参数化新方法,并结合这些超弦模型所具有的κ对称性给出了它们的卡当1-form,Maurer-Cartan方程,作用量和运动方程.     

Aspects of Pohlmeyer reduction for superstrings in AdS 5 × S 5

We review some recent work on Pohlmeyer reduced theory associated to superstring theory in AdS ₅ × S ⁵. We discuss the S-matrix of the reduced theory and also the computation of the 2-loop correction to the partition function in a non-trivial background.     

Moduli Space of IIB Superstring and SUYM in AdS5 × S5

This paper consists of two parts. In part I, we interpret the hidden symmetry of the moduli space of IIB superstring on AdS₅×S⁵ in terms of the chiral embedding in AdS₅, which turns out to be the CP³ conformal affine Toda model. We review how the position μ of poles in the Riemann-Hilbert formulation of dressing transformation and the value of loop parameter μ in the vertex operator of affine algebra determine the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinizes the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients μ of twistor. In part II, by extending the dressing symmetric action of IIB string in AdS₅×S⁵ to the D₃ brane, we find a gauged WZW action of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structures of left and right α-planes glue into an ambitwistor. The symmetry group of Nahm equations is centrally extended to an affine group, thus we explain why the spectral curve is given by affine Toda.     

Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals

Recently an infinite family of explicit Sasaki–Einstein metrics Y ^p,q on S ²×S ³ has been discovered, where p and q are two coprime positive integers, with q<p. These give rise to a corresponding family of Calabi–Yau cones, which moreover are toric. Aided by several recent results in toric geometry, we show that these are Kähler quotients namely the vacua of gauged linear sigma models with charges (p,p,?p+q,?p?q), thereby generalising the conifold, which is p=1,q=0. We present the corresponding toric diagrams and show that these may be embedded in the toric diagram for the orbifold for all q<p with fixed p. We hence find that the Y ^p,q manifolds are AdS/CFT dual to an infinite class of superconformal field theories arising as IR fixed points of toric quiver gauge theories with gauge group SU(N)^{2 p} . As a non–trivial example, we show that Y ^2,1 is an explicit irregular Sasaki–Einstein metric on the horizon of the complex cone over the first del Pezzo surface. The dual quiver gauge theory has already been constructed for this case and hence we can predict the exact central charge of this theory at its IR fixed point using the AdS/CFT correspondence. The value we obtain is a quadratic irrational number and, remarkably, agrees with a recent purely field theoretic calculation using a-maximisation.     

Free radicals in pyrimidines: E.S.R. of a γ-irradiated single crystal of 5-nitrouracil

Free radicals are observed in γ-irradiated single crystals of 5-nitrouracil with the unpaired electron showing hyperfine interaction with one nitrogen atom. The principal values of hyperfine coupling are A_x = 22·5 g, A_y = 25·2 g, and A_z = 40·0 g, and the principal values of the spectroscopic splitting factor are g_u = 2·0117, g_v = 2·0064 and g_w = 2·0027. The relationship of the directions of the corresponding principal axes to the molecular orientations show that the unpaired electron must be located in an sp ² orbital on either N₍₁₎ or N₍₅₎. Considerations of the mechanism of radical formation and comparison to radiation damage in other molecules make the N₍₁₎ location seem more probable. The π interaction of the nitro group on C₍₅₎ evidently prevents the formulation of free radicals with the unpaired electron on C₍₅₎. That carbon atom is the most common location of unpaired electron density in other pyrimidine free radicals.