It is shown that quantum one-loop potentials of the bulk fields in the Randall and Sundrum (RS) model may be immediately expressed in integrals with use of Barvinsky-Nesterov or equivalently Gelfand-Yaglom methods of calculation of quantum determinants. Simple expression is obtained for the UV-finite difference of one-loop quantum energies for two arbitrary values of parameter of the double-trace asymptotic boundary condition in one-brane and two-brane RS-models. Compact formula for Schwinger-DeWitt expansion gives values of induced Planck mass and induced gauge coupling constant in transverse space. S-DW expansion is plagued by IR-divergences in one-brane RS-model and makes sense in two-brane model.
We consider $α'$ corrections to the one-loop four-point correlator of the stress-tensor multiplet in $\mathcal{N}=4$ super Yang-Mills at order $1/N^4$. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS$_5\times$S$^5$. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop-amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the con…
We study the phases of scalar field theories in thermal $AdS_{d+1}$ spaces for $d=1,2,3$. The analysis is done for theories with global $O(N)$ symmetry for the finite as well as large $N$. The symmetry-preserving and symmetry-breaking phases are identified as a function of the mass-squared of the scalar field and temperature. On the way we also describe a method for computing one-loop partition function for scalar field on thermal $AdS_{d+1}$ for arbitrary $d$ that reproduces results known in the literature. The derivation is based on the method of images and uses the eigenfunctions of the Lap…
We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-$N$ conformal Gross Neveu model on $AdS_3$. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in Ad…
We discuss the string corrections to one-loop amplitudes in AdS$_5\times$S$^5$, focussing on their expressions in Mellin space. We present the leading $(α')^3$ corrections to the family of correlators $\langle \mathcal{O}_2 \mathcal{O}_2 \mathcal{O}_p \mathcal{O}_p \rangle$ at one loop and begin the exploration of the form of correlators with multiple channels. From these correlators we extract some string corrections to one-loop anomalous dimensions of families of operators of low twist.
We study the quasinormal modes (QNMs) of a charged scalar field on a Reissner-Nordström-anti-de Sitter (RN-AdS$_{5}$) black hole in the small radius limit by using the isomonodromic method. We also derive the low-temperature expansion of the fundamental QNM frequency. Finally, we provide numerical evidence that instabilities appear in the small radius limit for large values of the charge of the scalar field.
On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze
威尔逊圈是在AdS/CFT对应中计算的，方法是找到AdS_5 x S^5中弦运动方程的经典解，并计算其作用。一个重要的事实是，用来计算威尔逊圈的西格马模型是可积的，这一特征通过研究携带大量子数和自旋链的自旋弦而获得了相关性。我们应用相同的技术来解决方程的自旋字符串找到最小的曲面描述了广泛的一类威尔逊圈。我们集中在不同的情况下，周期边界条件的AdS_5和S^5因子，并找到了丰富的解决方案。我们研究的不同阶段出现的问题和评论的可积性的一般问题的适用性。
We report a result for the third-order correction in $1/N$ expansion to the four-point correlator of the stress tensor multiplet in $\mathcal{N}=4$ super Yang--Mills theory at large 't Hooft coupling, which corresponds to the two-loop scattering of four gravitons in the dual $\mathrm{AdS}_5\times\mathrm{S}^5$ supergravity. This is obtained by bootstrapping an educated ansatz based on intuitions from the hidden 10-dimensional conformal symmetry.
Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
我们计算了基本弦的精确单圈配分函数，这些弦的世界表面终止于AdS_4边界的一个尖点上，并且在CP ^[3]中有一个“跳跃”。这使我们能够在σ模型微扰理论中提取ABJM广义尖点反常维数Gamma_{cusp} ^{ABJM}（phi，theta）直到NLO的弦预测。通过类似的分析，我们给出了在AdS_4 x CP^3和AdS_3 x S^3 x S^3 x S^1背景中运动的折叠闭弦解的精确配分函数。将先前为AdS_5 x S^5对应物开发的工具应用于与AdS_4/CFT_3和AdS_3/CFT_2对应物相关的弦解，得到了结果。
Recent progresses in the computation of quantum string corrections to holographic Wilson loops are extended to the case of strings in $AdS_{4}\times CP^{3}$. For this, the ratio of 1/2-BPS circular and 1/6-BPS latitude fermionic Wilson loops in ABJM is considered at strong coupling by studying the corresponding semiclassical string partition functions. Explicit evaluation of fluctuation determinants using phaseshifts and diffeomorphism invariant regulators leads to exact matching with the recent field theory proposal. Key to this computation is the choice of boundary conditions for massless fe…
