Factorization of scattering is the hallmark of integrable 1+1 dimensional quantum field theories. For factorization of scattering to be possible the set of masses and momenta must be conserved in any two-to-two scattering process. We use this fact to constrain the form of the Ramond-Ramond fluxes for integrable supergravity anti-de Sitter backgrounds by analysing tree-level scattering of two AdS bosons into two fermions on the worldsheet of a BMN string. We find a condition which can be efficiently used to rule out integrability of AdS strings and therefore of the corresponding AdS/CFT dualities, as we demonstrate for some simple examples.
Relativistic limit on the $AdS_3 \times S^3 \times S^3 \times S^1$ string worldsheet
Università degli Studi di Padova（帕多瓦大学）；Universität Hamburg（汉堡大学）；University of Birmingham（伯明翰大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
我们导出了AdS_3 x S^3 x T^4上IIB超弦理论基本激发的非微扰世界面S矩阵.为此，我们研究了理论的离壳对称代数及其表示。我们用这些来确定S矩阵的标量因子，我们推导出这些标量因子满足的交叉方程。我们的治疗自动包括基本的无质量激发，消除了长期存在的障碍，使用可积性研究的AdS_3/CFT_2对应。本文包含了arXiv：1403.4543中首次公布的结果的详细推导。
The pure spinor formalism for the superstring can be formulated as a twisted N=2 worldsheet theory with fermionic generators $j_{BRST}$ and composite $b$ ghost. After untwisting the formalism to an N=1 worldsheet theory with fermionic stress tensor $j_{BRST}+b$, the worldsheet variables combine into N=1 worldsheet superfields $X^m$ and $Θ^α$ together with a superfield constraint relating $DX^m$ and $DΘ^α$. The constraint implies that the worldsheet superpartner of $θ^α$ is a bosonic twistor variable, and different solutions of the constraint give rise to the pure spinor or extended RNS formali…
We analyze the spectrum of perturbative closed strings on AdS3 x S3 x T4 with Ramond-Ramond flux using integrable methods. By solving the crossing equations we determine the massless and mixed-mass dressing factors of the worldsheet S matrix and derive the Bethe equations. Using these, we construct the underlying integrable spin chain and show that it reproduces the reducible spin chain conjectured at weak coupling in arXiv:1211.1952. We find that the string-theory massless modes are described by gapless excitations of the spin chain. The resulting degeneracy of vacua matches precisely the pro…
We revisit the calculation of the thermal free energy for string theory in three-dimensional anti-de Sitter spacetime with Neveu-Schwarz-Neveu-Schwarz flux. The path integral calculation is exploited to confirm the off-shell Hilbert space and we find that the Casimir of the discrete representations of the isometry group takes values in a half-open interval. We extend the free energy calculation to the case of superstrings, calculate the boundary toroidal twisted partition function in the Ramond-Ramond sector, and prove lower bounds on the boundary conformal dimension from the bulk perspective.…
In this PhD thesis we review some aspects of integrable models related to string backgrounds or their deformations. In the first part we develop methods to obtain exact results in the AdS3/CFT2 correspondence. We consider the AdS_3 x S^3 x T^4 background with pure Ramond-Ramond flux and we find the all-loop worldsheet S-matrix by exploiting the symmetries of the model in light-cone gauge. As we naturally include the massless modes on the worldsheet, we derive the full set of Bethe-Yang equations. In the massive sector we give also a spin-chain description and we write down solutions compatible…
From closed to open strings: the tensionless route in Kalb-Ramond background and noncommutativity
Yau Mathematical Sciences Center (YMSC), Tsinghua University（丘成桐数学科学中心，清华大学）；Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里什-昌德拉研究所，霍米·巴巴国家研究所成员机构）
We study finite temperature string scale $AdS_3$ backgrounds. One background is $AdS_3 \times S^1 \times T^2$ in which the anti-de Sitter space-time and the circle are at the radius $\sqrt{α'}$. Using path integral techniques, we show that the bulk spectrum includes a continuum of states as well as Ramond-Ramond ground states that agree with those of the symmetric orbifold of the two-torus after second quantization. We also examine the one-loop free energy of the background $AdS_3 \times S^1$ at curvature radius $\sqrt{2 α'/3}$. In the space-time NSNS sector, the string theory spontaneously br…
We find the Yangian symmetry underlying the integrability of type IIB superstrings on $AdS_3 \times S^3 \times S^3 \times S^1$ with mixed Ramond-Ramond and Neveu-Schwarz-Neveu-Schwarz flux. The abstract commutation relations of the Yangian are formulated via RTT realisation, while its matrix realisation is in an evaluation representation depending on the quantised coefficient of the Wess-Zumino term. The construction naturally encodes a secret symmetry of the worldsheet scattering matrix whose generators map different Yangian levels to each other. We show that in the large effective string ten…
On the $AdS_3\times S^3\times S^3\times S^1$ dressing factors
Hamilton Mathematics Institute and School of Mathematics Trinity College, Dublin 2, Ireland（都柏林三一学院数学与哈密顿数学研究所）；University of Padova, Italy（帕多瓦大学）；School of Mathematics, University of Birmingham, Edgbaston B15 2TT, UK（伯明翰大学数学学院）；Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, 35131 Padova, Italy（意大利国家核物理研究所帕多瓦分部）
We study n-string scattering amplitudes in three-dimensional Anti-de Sitter space (AdS3). We focus our attention on the processes in which the winding number conservation is violated maximally; that is, those processes in which it is violated in n-2 units. A worldsheet conformal field theory calculation leads us to confirm a previous conjecture about the functional form of these observables.
In this paper, which is the last of a series of three, we first verify that the two open-closed effective potentials derived in the previous paper from the WZW theory in the large Hilbert space and the $A_\infty$ theory in the small Hilbert space have the same vacuum structure. In particular, we show that mass-term deformations given by the effective (two open)-(one closed) couplings are the same, provided the effective tadpole is vanishing to first order in the closed string deformation. We show that this condition is always realized when the worldsheet BCFT enjoys a global ${\cal N}=2$ super…
Nonrelativistic string theory is a unitary, ultraviolet finite quantum gravity theory with a nonrelativistic string spectrum. The vertex operators of the worldsheet theory determine the spacetime geometry of nonrelativistic string theory, known as the string Newton-Cartan geometry. We compute the Weyl anomaly of the nonrelativistic string worldsheet sigma model describing strings propagating in a string Newton-Cartan geometry, Kalb-Ramond and dilaton background. We derive the equations of motion that dictate the backgrounds on which nonrelativistic string theory can be consistently defined qua…
We consider the exact $R$-matrix of $AdS_3/CFT_2$, which is the building block for describing the scattering of worldsheet excitations of the light-cone gauge-fixed backgrounds $AdS_3 \times S^3 \times T^4$ and $AdS_3 \times S^3 \times S^3 \times S^1$ with pure Ramond-Ramond fluxes. We show that $R$ is invariant under a "deformed boost" symmetry, for which we write an explicit exact coproduct, i.e. its action on 2-particle states. When we include the boost, the symmetries of the $R$-matrix close into a $q$-Poincaré superalgebra. Our findings suggest that the recently discovered boost invarianc…
