arXiv subjects

L. Hoffmann

Publications and source records attributed to L. Hoffmann.

7 recordsLinked to original sources

arXiv2020

Table-top Nonlinear Extreme Ultraviolet Spectroscopy

The lack of available table-top extreme ultraviolet (XUV) sources with high enough fluxes and coherence properties have limited the availability of nonlinear XUV and x-ray spectroscopies to free electron lasers (FEL). Here, we demonstrate second harmonic generation (SHG) on a table-top XUV source for the first time by observing SHG at the Ti M2,3-edge with a high harmonic seeded soft x-ray laser (HHG-SXRL) [1,2]. Further, this experiment represents the first SHG experiment in the XUV. First-principles electronic structure calculations are used to confirm the surface specificity and resonant enhancement of the SHG signal. The realization of XUV-SHG on a table-top source with femtosecond temporal resolution opens up tremendous opportunities for the study of element-specific dynamics in multi-component systems where surface, interfacial, and bulk-phase asymmetries play a driving role in smaller-scale labs as opposed to FELs.

physics.optics↗

arXiv2001

Multi-trace quasi-primary fields of $\mathcal{N}=4$ $SYM_4$ from AdS n-point functions

We develop a recursive algorithm for the investigation of infinite sequences of quasi-primary fields obtained from chiral primary operators (CPOs) $O^I_k(x)$ and eventually their derivatives by applying operator product expansions and singling out SO(6) representations. We show that normal products of $O_2$ operators can be expressed in terms of projection operators on representations of SO(20) and discuss intertwining operators for SO(6) representations. Furthermore we derive $\mathcal{O}(\frac{1}{N^2})$ corrections to AdS/CFT 4-point functions by graphical combinatorics and finally extract anomalous dimensions by applying the method of conformal partial wave analysis. We find infinite sequences of quasi-primary fields with vanishing anomalous dimensions and interpret them as 1/2-BPS or 1/4-BPS fields.

hep-th↗

arXiv2001

Composite fields, generalized hypergeometric functions and the $U(1)_Y$ symmetry in the AdS/CFT correspondence

We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of $U(1)_Y$ symmetry for four-point functions.

hep-th↗

arXiv2001

Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions

Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tildeΦ\tildeΦ$, $\tilde{C}\tilde{C}$ and $\tildeΦ\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $δ=2+l$ or $8+l+η(l)$ and $η(l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $δ=λ+l+η(l)$ with $λ\geq 10$. The anomalous dimensions $η(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tildeΦ\tildeΦ + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tildeΦ\tilde{C} + \tilde{C}\tildeΦ)$ and are found to be the same, proving $U(1)_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.

hep-th↗

arXiv2000

Aspects of the conformal operator product expansion in AdS/CFT correspondence

We present a detailed analysis of a scalar conformal four-point function obtained from AdS/CFT correspondence. We study the scalar exchange graphs in AdS and discuss their analytic properties. Using methods of conformal partial wave analysis, we present a general procedure to study conformal four-point functions in terms of exchanges of scalar and tensor fields. The logarithmic terms in the four-point functions are connected to the anomalous dimensions of the exchanged fields. Comparison of the results from AdS graphs with the conformal partial wave analysis, suggests a possible general form for the operator product expansion of scalar fields in the boundary CFT.

hep-th↗

arXiv2000

AdS Box Graphs, Unitarity and Operator Product Expansions

We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis.

hep-th↗

arXiv2000

A note on the analyticity of AdS scalar exchange graphs in the crossed channel

We discuss the analytic properties of AdS scalar exchange graphs in the crossed channel. We show that the possible non-analytic terms drop out by virtue of non-trivial properties of generalized hypergeometric functions. The absence of non-analytic terms is a necessary condition for the existence of an operator product expansion for CFT amplitudes obtained from AdS/CFT correspondence.

hep-th↗