Chaos and the reparametrization mode on the AdS2_2 string

We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS$_2$ geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS$_2$ black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS$_2$ string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to $SL(2,\mathbb{R})$ invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in ${\cal N}=4$ SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling.Comment: 66 + 21 pages, 4 figures; v2 Added figures 2, 3, and 5, clarified discussions in section 3 and section 6.3, and made additional minor edits. Results unchange

Boundary reparametrizations and six-point functions on the AdS2_2 string

We compute the tree-level connected six-point function of identical scalar fluctuations of the AdS$_2$ string worldsheet dual to the half-BPS Wilson line in planar ${\cal N}=4$ Super Yang-Mills. The calculation can be carried out analytically in the conformal gauge approach, where the boundary reparametrization mode of the string plays a crucial role. We also study the analytic continuation of the six-point function to an out-of-time-order configuration, which is related to a 3-to-3 scattering amplitude in flat space. As a check of our results, we also numerically compute the six-point function using the Nambu-Goto action in static gauge, finding agreement with the conformal gauge answer.Comment: 52 pages, 8 figure

Interaction between anandamide and sphingosine-1-phosphate in mediating vasorelaxation in rat coronary artery

<b>BACKGROUND AND PURPOSE</b> Anandamide and sphingosine-1-phosphate (S1P) both regulate vascular tone in a variety of vessels. This study aimed to examine the mechanisms involved in the regulation of coronary vascular tone by anandamide and S1P, and to determine whether any functional interaction occurs between these receptor systems. <br></br> <b>EXPERIMENTAL APPROACH</b> Mechanisms used by anandamide and S1P to regulate rat coronary artery (CA) reactivity were investigated using wire myography. Interactions between S1P and the cannabinoid (CB)2 receptor were determined using human embryonic kidney 293 (HEK293) cells that stably over-express recombinant CB2 receptor. <br></br> <b>KEY RESULTS</b> Anandamide and S1P induced relaxation of the rat CA. CB2 receptor antagonists attenuated anandamide-induced relaxation, while S1P-mediated relaxation was dependent on the vascular endothelium and S1P3. Anandamide treatment resulted in an increase in the phosphorylation of sphingosine kinase-1 within the CA. Conversely, anandamide-mediated relaxation was attenuated by inhibition of sphingosine kinase. Moreover, S1P3, specifically within the vascular endothelium, was required for anandamide-mediated vasorelaxation. In addition to this, S1P-mediated relaxation was also reduced by CB2 receptor antagonists and sphingosine kinase inhibition. Further evidence that S1P functionally interacts with the CB2 receptor was also observed in HEK293 cells over-expressing the CB2 receptor. <br></br> <b>CONCLUSIONS AND IMPLICATIONS</b> In the vascular endothelium of rat CA, anandamide induces relaxation via a mechanism requiring sphingosine kinase-1 and S1P/S1P3. In addition, we report that S1P may exert some of its effects via a CB2 receptor- and sphingosine kinase-dependent mechanism, where subsequently formed S1P may have privileged access to S1P3 to induce vascular relaxation

The endocannabinoid anandamide causes endothelium-dependent vasorelaxation in human mesenteric arteries

The endocannabinoid anandamide (AEA) causes vasorelaxation in animal studies. Although circulating AEA levels are increased in many pathologies, little is known about its vascular effects in humans. The aim of this work was to characterise the effects of AEA in human arteries. Ethical approval was granted to obtain mesenteric arteries from patients (n = 31) undergoing bowel resection. Wire myography was used to probe the effects and mechanisms of action of AEA. RT‐PCR was used to confirm the presence of receptor mRNA in human aortic endothelial cells (HAECs) and intracellular signalling proteins were measured using multiplex technology. AEA caused vasorelaxation of precontracted human mesenteric arteries with an Rmax of ∼30%. A synthetic CB1 agonist (CP55940) caused greater vasorelaxation (Rmax ∼60%) while a CB2 receptor agonist (HU308) had no effect on vascular tone. AEA-induced vasorelaxation was inhibited by removing the endothelium, inhibition of nitric oxide (NO) synthase, antagonising the CB1 receptor and antagonising the proposed novel endothelial cannabinoid receptor (CBe). AEA‐induced vasorelaxation was not affected by CB2 antagonism, by depleting sensory neurotransmitters, or inhibiting cyclooxygenase activity. RT‐PCR showed CB1 but not CB2 receptors were present in HAECs, and AEA and CP55940 had similar profiles in HAECs (increased phosphorylation of JNK, NFκB, ERK, Akt, p70s6K, STAT3 and STAT5). Post hoc analysis of the data set showed that overweight patients and those taking paracetamol had reduced vasorelaxant responses to AEA. These data show that AEA causes moderate endothelium-dependent, NO-dependent vasorelaxation in human mesenteric arteries via activation of CB1 receptors

Half-BPS Wilson Loops in AdS/CFT

The Maldacena-Wilson loop is a versatile gauge-invariant non-local operator that can be used to probe the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. When the contour is a straight line or a circle, the Wilson loop preserves half the superconformal symmetries and can be calculated in $\mathcal{N}=4$ super Yang-Mills (SYM) in the planar limit using perturbation theory or for all values of the coupling and rank of the gauge group using supersymmetric localization. In the supergravity regime, the dual object in $AdS_5$ is the surface of minimal area that is incident on the Wilson loop on the boundary. Part I of this thesis rederives many of the classic results involving the expectation value of the circular Wilson loop on both the CFT and AdS sides of AdS/CFT. The summation of ladder diagrams in perturbation theory is carried out in detail. The necessary random matrix tools--- including Faddeev-Popov gauge fixing, the method of orthogonal polynomials and the saddle point approximation--- are developed and used to evaluate the integrals over Hermitian matrices and imaginary Hermitian matrices that represent the expectation values of the $U(N)$ and $SO(N)$ circular Wilson loops. Part I also carries out a novel confirmation of AdS/CFT by calculating the large $N$, large $\lambda$ limit of the $SO(N)$ Wilson loop in the spinor representation and replicating the result in AdS by minimizing the volume of a D5-brane wrapped on an $\mathbb{R}P^4$ subspace of $AdS_5\times \mathbb{R}P^5$ and incident on the Wilson loop. Shifting focus, Part II of the thesis explores the $AdS_2/CFT_1$ correspondence connecting the field theory characterizing fluctuations of the $AdS_2$ minimal surface to the one-dimensional defect conformal field theory living on the straight Wilson line. The four-point functions of protected composite defect primaries are calculated and used to extract operator product expansion (OPE) data for the defect CFT. The anomalous dimensions of conglomerated operators appearing in the OPE of two composite primaries are determined, some of which are checked by looking at the two-point functions of the conglomerated operators using point-splitting regularization. There is evidence of universal properties of the anomalous dimensions, as well as hints of not-yet-understood structure underlying the defect CFT, which may be illuminated in future work

Wilson loops in N \mathcal{N} = 4 SO(N) SYM and D-branes in AdS5 × ℝℙ5

Abstract We study the half-BPS circular Wilson loop in $$\mathcal{N}$$ N = 4 super Yang-Mills with orthogonal gauge group. By supersymmetric localization, its expectation value can be computed exactly from a matrix integral over the Lie algebra of SO(N). We focus on the large N limit and present some simple quantitative tests of the duality with type IIB string theory in AdS5× ℝℙ5. In particular, we show that the strong coupling limit of the expectation value of the Wilson loop in the spinor representation of the gauge group precisely matches the classical action of the dual string theory object, which is expected to be a D5-brane wrapping a ℝℙ4 subspace of ℝℙ5. We also briefly discuss the large N, large λ limits of the SO(N) Wilson loop in the symmetric/antisymmetric representations and their D3/D5-brane duals. Finally, we use the D5-brane description to extract the leading strong coupling behavior of the “bremsstrahlung function” associated to a spinor probe charge, or equivalently the normalization of the two-point function of the displacement operator on the spinor Wilson loop, and obtain agreement with the localization prediction.</jats:p

Chaos and the reparametrization mode on the AdS2 string

Abstract We study the holographic correlators corresponding to scattering of fluctuations of an open string worldsheet with AdS2 geometry. In the out-of-time-order configuration, the correlators display a Lyapunov growth that saturates the chaos bound. We show that in a double-scaling limit interpolating between the Lyapunov regime and the late time exponential decay, the out-of-time-order correlator (OTOC) can be obtained exactly, and it has the same functional form found in the analogous calculation in JT gravity. The result can be understood as coming from high energy scattering near the horizon of a AdS2 black hole, and is essentially controlled by the flat space worldsheet S-matrix. While previous works on the AdS2 string employed mainly a static gauge approach, here we focus on conformal gauge and clarify the role of boundary reparametrizations in the calculation of the correlators. We find that the reparametrization mode is governed by a non-local action which is distinct from the Schwarzian action arising in JT gravity, and in particular leads to SL(2, ℝ) invariant boundary correlators. The OTOC in the double-scaling limit, however, has the same functional form as that obtained from the Schwarzian, and it can be computed using the reparametrization action and resumming a subset of diagrams that are expected to dominate in the limit. One application of our results is to the defect CFT defined by the half-BPS Wilson loop in N $$\mathcal{N}$$ = 4 SYM. In this context, we show that the exact result for the OTOC in the double-scaling limit is in precise agreement with a recent analytic bootstrap prediction to three-loop order at strong coupling