Tailoring Three-Point Functions and Integrability III. Classical Tunneling

Tailoring Three-Point Functions and Integrability

We use Integrability techniques to compute structure constants in N=4 SYM to leading order. Three closed spin chains, which represent the single trace gauge-invariant operators in N=4 SYM, are cut into six open chains which are then sewed back together into some nice pants, the three-point function. The algebraic and coordinate Bethe ansatz tools necessary for this task are reviewed. Finally, we discuss the classical limit of our results, anticipating some predictions for quasi-classical string correlators in terms of algebraic curves.

Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match

We compute three-point functions of single trace operators in planar N=4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.

Tailoring Three-Point Functions and Integrability IV. Theta-morphism

We compute structure constants in N=4 SYM at one loop using Integrability. This requires having full control over the two loop eigenvectors of the dilatation operator for operators of arbitrary size. To achieve this, we develop an algebraic description called the Theta-morphism. In this approach we introduce impurities at each spin chain site, act with particular differential operators on the standard algebraic Bethe ansatz vectors and generate in this way higher loop eigenvectors. The final results for the structure constants take a surprisingly simple form. For some quantities we conjecture …

Tailoring Non-Compact Spin Chains

We study three-point correlation functions of local operators in planar $\mathcal{N}=4$ SYM at weak coupling using integrability. We consider correlation functions involving two scalar BPS operators and an operator with spin, in the so called SL(2) sector. At tree level we derive the corresponding structure constant for any such operator. We also conjecture its one loop correction. To check our proposals we analyze the conformal partial wave decomposition of known four-point correlation functions of BPS operators. In perturbation theory, we extract from this decomposition sums of structure con…

Integrability of the $ν=4/3$ fractional quantum Hall edge states

We investigate the homogeneous chiral edge theory of the filling $ν=4/3$ fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We identify two solvable cases: one case where the theory gives two free chiral boson modes, and the other case where the theory yields one free charge $\frac{2e}{\sqrt{3}}$ chiral fermion and two free chiral Bogoliubov (Majorana) fermions. For generic parameters, the energy spectrum from our exact diagonalization shows Poisson level spacing statistics (LSS) in each c…

量子杂质问题中红外不动点的扰动和对偶性

Perturbation of infra-red fixed points and duality in quantum impurity problems

在本文中，我们解释了如何一个有意义的无关微扰理论周围的红外（强耦合）不动点可以进行可积量子杂质问题。这是详细说明的自旋1/2近藤模型，我们的方法引起的电阻率的完全低温膨胀，超出了众所周知的$T^2$费米液体的行为。我们还考虑了边缘态隧穿问题，并证明了Keldysh技术的直流电流满足一个确切的对偶之间的UV和IR制度。这在物理上对应于劳克林准粒子和电子隧穿之间的对偶性，更正式地说，对应于存在精确的瞬子膨胀。对偶性与可积性紧密相连，并且不可能是先验的。