An Insight Into Asymmetric Synthesis and Bioorganic Applications of Novel Cα- Methyl-Lysine, - Proline, - Nipocotic Acid Analogues

Prochiral malonic diesters consisting of a quaternary carbon center have been successfully converted into a different set of tBoc-Fmoc-α2,2-methyllysine-OH analogues through chiral malonic half-ester intermediates achieved via enzymatic (Pig Liver Esterase, PLE) hydrolysis. The selection of chiral half-ester intermediates, which vary from 1 to 6 methylene units in the side chain, are achieved in high optical purity (92% - 97% ee) and in good yields (65% - 72%). The PLE hydrolysis of malonic diesters with a variety of side chain lengths observed to obey the Jones’s PLE model as evidenced from the stereochemical configurations of the resulting chiral half-esters. The optimized synthetic strategy allows the construction of both enantiomers of α2,2-methyllysine analogues, and a (S)-β2,2-methyllysine analogue from a common synthon by straightforward exploitation of protecting groups. Two different straightforward synthetic strategies are illustrated for the synthesis of α2,2-methyllysine analogues. The described strategies should find significant usefulness in preparing novel peptide libraries with unnatural lysine analogues. A Vapreotide analogue incorporating (S)-α2,2-methyllysine was constructed. However, the Vapreotide analogue with (S)-α-methyl-α-lysine is found to lose its specific binding to somatostatin receptor subtype 2 (SSTR2). In an additional project, a stereoselective and enantiodivergent cyclization strategy for the preparation of γ/δ-lactams is exhibited. The cyclization strategy exploits chiral malonic esters prepared from enantiomerically enriched (92% ee - 97% ee) mono esters of disubstituted malonic acid. The cyclization takes place with the selective departure of a substituted benzyl alcohol as the leaving group. A Hammett study demonstrates that the cyclization is under electronic control. The resulting γ/δ-lactam was readily converted into a novel proline/nipecotic acid analogue

A Note on Charged Black Holes in AdS space and the Dual Gauge Theories

We study the thermodynamics and the phase structures of Reissner-Nordstrom and Born-Infeld black holes in AdS space by constructing ``off-shell'' free energies using thermodynamic quantities derived directly from the action. We then use these results to propose ``off-shell'' effective potentials for the respective boundary gauge theories. The saddle points of the potentials describe all the equilibrium phases of the gauge theories.Comment: LaTeX, 21+1 pages, 7 figure

A note on AdS cosmology and gauge theory correlator

Using AdS/CFT prescription, we compute two point Yang-Mills correlator on a constant time slice for the Kasner background. Pushing the surface close to the initial singularity, we find, in some cases, the correlator does not develop pole. This is consistent with the observations made in a recent work. We further numerically calculate similar correlator where the bulk is a Kasner AdS soliton. We find that the qualitative behaviour of the correlator remains unchanged.Comment: 17 pages, 2 figures, journal versio

Non-supersymmetric Microstates of the MSW System

We present an analysis parallel to that of Giusto, Ross, and Saxena (arXiv:0708.3845) and construct a discrete family of non-supersymmetric microstate geometries of the Maldacena-Strominger-Witten system. The supergravity configuration in which we look for the smooth microstates is constructed using SO(4,4) dualities applied to an appropriate seed solution. The SO(4,4) approach offers certain technical advantages. Our microstate solutions are smooth in five dimensions, as opposed to all previously known non-supersymmetric microstates with AdS3 cores, which are smooth only in six dimensions. The decoupled geometries for our microstates are related to global AdS3 x S2 by spectral flows.Comment: 38 pages, including appendices and references; v2 refs + one paragraph adde

A universal approach to Krylov State and Operator complexities

We present a general framework in which both Krylov state and operator complexities can be put on the same footing. In our formalism, the Krylov complexity is defined in terms of the density matrix of the associated state which, for the operator complexity, lives on a doubled Hilbert space obtained through the channel-state map. This unified definition of complexity in terms of the density matrices enables us to extend the notion of Krylov complexity, to subregion or mixed state complexities and also naturally to the Krylov mutual complexity. We show that this framework also encompasses nicely the holographic notions of complexity.Comment: 12 pages, typos corrected, references adde

A toy model of black hole complementarity

We consider the algebra of simple operators defined in a time band in a CFT with a holographic dual. When the band is smaller than the light crossing time of AdS, an entire causal diamond in the center of AdS is separated from the band by a horizon. We show that this algebra obeys a version of the Reeh-Schlieder theorem: the action of the algebra on the CFT vacuum can approximate any low energy state in the CFT arbitrarily well, but no operator within the algebra can exactly annihilate the vacuum. We show how to relate local excitations in the complement of the central diamond to simple operators in the band. Local excitations within the diamond are invisible to the algebra of simple operators in the band by causality, but can be related to complicated operators called "precursors". We use the Reeh-Schlieder theorem to write down a simple and explicit formula for these precursors on the boundary. We comment on the implications of our results for black hole complementarity and the emergence of bulk locality from the boundary.Comment: 24 page

The dark bubbleography

We present the holographic construction of the dark bubble model of dark energy and highlight the pivotal role played by the non-normalizable modes. Following the route of holographic renormalization, we show that the non-normalizable modes are essential for having a vanishing mass for the induced graviton in any braneworld model. We then apply this idea in the computation of the propagator on the wall of the dark bubble introduced in 1807.01570.Comment: 1+14 page