Nonperturbative Matching Between Equal-Time and Lightcone Quantization

We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of $\lambda \phi^4$ theory in $d=2$. We discuss the perturbative matching between bare parameters and the failure of its naive nonperturbative extension. We argue that they are nevertheless the same theory nonperturbatively, and that furthermore the nonperturbative map between bare parameters can be extracted from ET perturbation theory via Borel resummation of the mass gap. We test this map by using it to compare physical quantities computed using numerical Hamiltonian truncation methods in ET and LC.Comment: 22+8 pages, 10 figure

Hawking from Catalan

The Virasoro algebra determines all `graviton' matrix elements in AdS$_3$/CFT$_2$. We study the explicit exchange of any number of Virasoro gravitons between heavy and light CFT$_2$ operators at large central charge. These graviton exchanges can be written in terms of new on-shell tree diagrams, organized in a perturbative expansion in $h_H/c$, the heavy operator dimension divided by the central charge. The Virasoro vacuum conformal block, which is the sum of all the tree diagrams, obeys a differential recursion relation generalizing that of the Catalan numbers. We use this recursion relation to sum the on-shell diagrams to all orders, computing the Virasoro vacuum block. Extrapolating to large $h_H/c$ determines the Hawking temperature of a BTZ black hole in dual AdS$_3$ theories.Comment: 19+8 pages, 5 figure

Finite Element Analysis of Laser Peening of Thin Aluminum Structures

Laser shock peening has become a commonly applied industrial surface treatment, particularly for high-strength steel and titanium components. Effective application to aluminum alloys, especially in the thin sections common in aerospace structures, has proved more challenging. Previous work has shown that some peening conditions can introduce at-surface tensile residual stress in thin Al sections. In this study, we employ finite element modeling to identify the conditions that cause this to occur, and show how these adverse effects can be mitigated through selection of peen parameters and patterning

Eikonalization of Conformal Blocks

Classical field configurations such as the Coulomb potential and Schwarzschild solution are built from the t-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the `eikonalization' of conformal blocks. We show that when an operator $T$ appears in the OPE $\mathcal{O}(x) \mathcal{O}(0)$, then the large spin $\ell$ Fock space states $[TT \cdots T]_{\ell}$ also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an $\langle \mathcal{O} \mathcal{O} \mathcal{O} \mathcal{O} \rangle$ correlator build the classical `$T$ field' in the dual AdS description. In some limits the sum of all Fock space exchanges can be represented as the exponential of a single $T$ exchange in the 4-pt correlator of $\mathcal{O}$. Our results should be useful for systematizing $1/\ell$ perturbation theory in general CFTs and simplifying the computation of large spin OPE coefficients. As examples we obtain the leading $\log \ell$ dependence of Fock space conformal block coefficients, and we directly compute the OPE coefficients of the simplest `triple-trace' operators.Comment: 32+17 pages, 6 figures; references added, discussion of eikonal limit clarifie

Virasoro Conformal Blocks and Thermality from Classical Background Fields

We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in $AdS_3$, or equivalently, the eigenstate thermalization hypothesis for $CFT_2$ at large central charge.Comment: 27+7 pages, 3 figures; typos corrected, citations adde

Lessons from crossing symmetry at large N

20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe

THE SYNERGY BETWEEN SUBSECTOR COMPETITIVENESS AND REGIONAL DEVELOPMENT: THE CASE OF TURKEY AND THE TOMATO SUBSECTOR

Abstract This study develops a conceptual model of the institutions and key factors that facilitate competitiveness on the national and subsector level and then determines how linkages between the factors that enhance competitiveness and regional development can be created. Turkey and the Turkish tomato subsector provided the case to test this model.Regional development, sustainable competitiveness, tomato processing industry, Turkey, industry clusters, Community/Rural/Urban Development,

Universality of Long-Distance AdS Physics from the CFT Bootstrap

We begin by explicating a recent proof of the cluster decomposition principle in AdS_{d+1} from the CFT_d bootstrap in d > 2. The CFT argument also computes the leading interactions between distant objects in AdS, and we confirm the universal agreement between the CFT bootstrap and AdS gravity in the semi-classical limit. We proceed to study the generalization to 2d CFTs, which requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit. We compute these blocks in a semiclassical, large central charge approximation, and use them to prove a suitably modified theorem. In particular, from the 2d bootstrap we prove the existence of large spin operators with fixed 'anomalous dimensions' indicative of the presence of deficit angles in AdS_3. As we approach the threshold for the BTZ black hole, interpreted as a CFT scaling dimension, the twist spectrum of large spin operators becomes dense. Due to the exchange of the Virasoro identity block, primary states above the BTZ threshold mimic a thermal background for light operators. We derive the BTZ quasi-normal modes, and we use the bootstrap equation to prove that the twist spectrum is dense. Corrections to thermality could be obtained from a more refined computation of the Virasoro conformal blocks.Comment: 34+31 pages, references added, typo in higher-dimensional energy shift corrected, discussion of coefficient density bounds expande

System configuration and executive requirements specifications for reusable shuttle and space station/base

System configuration and executive requirements specifications for reusable shuttle and space station/bas