scholarly journals Degenerate operators in JT and Liouville (super)gravity

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Thomas G. Mertens
Keyword(s):  
Partition Function ◽  
Perturbation Series ◽  
Point Function ◽  
First Order ◽  
Fixed Length ◽  
Higher Genus ◽  
Degenerate Operators ◽  
Shed Light ◽  
Explicit Expressions

Abstract We derive explicit expressions for a specific subclass of Jackiw-Teitelboim (JT) gravity bilocal correlators, corresponding to degenerate Virasoro representations. On the disk, these degenerate correlators are structurally simple, and they allow us to shed light on the 1/C Schwarzian bilocal perturbation series. In particular, we prove that the series is asymptotic for generic weight h ∉ −ℕ/2. Inspired by its minimal string ancestor, we propose an expression for higher genus corrections to the degenerate correlators. We discuss the extension to the $$ \mathcal{N} $$ N = 1 super JT model. On the disk, we similarly derive properties of the 1/C super-Schwarzian perturbation series, which we independently develop as well. As a byproduct, it is shown that JT supergravity saturates the chaos bound λL = 2π/β at first order in 1/C. We develop the fixed-length amplitudes of Liouville supergravity at the level of the disk partition function, the bulk one-point function and the boundary two-point functions. In particular we compute the minimal superstring fixed length boundary two-point functions, which limit to the super JT degenerate correlators. We give some comments on higher topology at the end.

From Autonomy to Heautonomy

2020 ◽  
Vol 50 (3) ◽  
pp. 261-274
Author(s):  
Jörg Noller ◽  
Keyword(s):  
Second Order ◽  
Self Determination ◽  
Individual Freedom ◽  
Moral Law ◽  
First Order ◽  
Shed Light

In this paper, I will shed light on Karl Leonhard Reinhold’s and Friedrich Schiller’s conceptions of practical self-determination after Kant. First, I outline Kant’s conception of freedom as autonomy. I then explain the so-called “Reinhold’s dilemma,” which concerns the problem of moral imputability in the case of immoral actions, which arises from Kant’s theory of autonomy. I then show how Reinhold and Schiller tried to escape this dilemma by developing an elaborated theory of individual freedom. I will argue that Reinhold’s and Schiller’s symmetrical account of freedom to act according and against the moral law is not to be confused with freedom of indifference but can be reconstructed in terms of practical self-determination on the basis of first-order desires and second-order volitions.

Self-consistent perturbation treatment of impurities and imperfections in metals

1961 ◽  
Vol 261 (1304) ◽  
pp. 119-133 ◽  
Keyword(s):  
Free Electron ◽  
Plane Waves ◽  
Present Theory ◽  
Bloch Wave ◽  
Perturbation Series ◽  
Order Method ◽  
First Order ◽  
Hartree Potential ◽  
Self Consistent ◽  
First Order Method

A full perturbation treatment of the Dirac density matrix is developed as a basis for selfconsistent calculations in free-electron metals containing localized defects. The present perturbation series is shown to sum to the well-known result for the case of slowly varying potentials. To first order in perturbation theory, exact self-consistent results for the radial density of displaced charge and the Hartree potential in the presence of point singularities have been obtained over a density range sufficient to cover all metals under normal conditions. The basic limitations of Mott’s first-order method, based on the assumption of slowly varying potentials, are shown to be completely removed and the self-consistent density and potential display long-range oscillations. Finally, the application of the present approach to Bloch wave functions rather than plane waves is briefly considered. Friedel’s generalized first-order method, applicable to a band structure, may be obtained from the present theory for sufficiently slowly varying potentials. Unfortunately, such an assumption is seen by comparison with the free-electron findings to lead to serious errors.

scholarly journals GAUGE INVARIANT ACTION FOR THE OPEN BOSONIC STRING

2008 ◽  
Vol 23 (07) ◽  
pp. 1001-1017 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Partition Function ◽  
Gauge Invariance ◽  
Taylor Expansion ◽  
Bosonic String ◽  
Point Function ◽  
Gauge Invariant ◽  
Invariant Action ◽  
Pole Structure ◽  
Zero Momentum ◽  
String Amplitudes

The issue of space–time gauge invariance for the bosonic string has been earlier addressed using the loop variable formalism. In this paper the question of obtaining a gauge invariant action for the open bosonic string is discussed. The derivative with respect to ln a (where a is a worldsheet cutoff) of the partition function — which is first normalized by dividing by the integral of the two-point function of a marginal operator — is a candidate for the action. Applied to the zero-momentum tachyon it gives a tachyon potential that is similar to those that have been obtained using Witten's background independent formalism. This procedure is easily made gauge invariant in the loop variable formalism by replacing ln a by Σ which is the generalization of the Liouville mode that occurs in this formalism. We also describe a method of resumming the Taylor expansion that is done in the loop variable formalism. This allows one to see the pole structure of string amplitudes that would not be visible in the original loop variable formalism.

LEVEL-ONE SU(N) WZNW MODELS ON HIGHER-GENUS RIEMANN SURFACES

1993 ◽  
Vol 08 (17) ◽  
pp. 2955-2972 ◽  
Author(s):  
M. ALIMOHAMMADI ◽  
H. ARFAEI
Keyword(s):  
Partition Function ◽  
Simple Form ◽  
Riemann Surfaces ◽  
Theta Functions ◽  
Modular Invariance ◽  
Fusion Rules ◽  
Group Manifold ◽  
Special Cases ◽  
Wznw Model ◽  
Higher Genus

Using factorization properties and fusion rules, we find the higher-genus partition function and two-point correlators for the SU (N)1 WZNW model. The result has simple form in terms of higher-genus theta functions on the group manifold. The previously known results of SU (2)1 and SU (3)1 are also obtained as special cases. This method, combined with other considerations such as modular invariance, can be extended to the nonsimply laced groups and higher-level WZNW models.

scholarly journals Working equation of LR-TD-DFT First-order polarization propagator approximation

2021 ◽  
Author(s):  
Jacob Pedersen ◽  
Kurt Mikkelsen
Keyword(s):  
Electronic Structure ◽  
Density Functional ◽  
Matrix Elements ◽  
First Order ◽  
Polarization Propagator ◽  
Functional Representation ◽  
Td Dft ◽  
Response Method ◽  
Detailed Derivation ◽  
Explicit Expressions

We present the derivation of a new response method termed rst order po- larization propagator approximation. The electronic structure is given by a density functional representation. We provide a detailed derivation of the method along with explicit expressions for the relevant integrals and matrix elements.

scholarly journals ϵ-CORRECTED SEIBERG–WITTEN PREPOTENTIAL OBTAINED FROM HALF-GENUS EXPANSION IN β-DEFORMED MATRIX MODEL

2011 ◽  
Vol 26 (20) ◽  
pp. 3439-3467 ◽  
Author(s):  
H. ITOYAMA ◽  
N. YONEZAWA
Keyword(s):  
Free Energy ◽  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Partition Function ◽  
Matrix Model ◽  
Conformal Block ◽  
Supersymmetric Gauge ◽  
Genus Expansion ◽  
Resolvent Function ◽  
Explicit Expressions

We consider the half-genus expansion of the resolvent function in the β-deformed matrix model with three-Penner potential under the AGT conjecture and the 0d–4d dictionary. The partition function of the model, after the specification of the paths, becomes the DF conformal block for fixed c and provides the Nekrasov partition function expanded both in [Formula: see text] and in ϵ = ϵ1+ϵ2. Exploiting the explicit expressions for the lower terms of the free energy extracted from the above expansion, we derive the first few ϵ corrections to the Seiberg–Witten prepotential in terms of the parameters of SU(2), Nf = 4, [Formula: see text] supersymmetric gauge theory.

scholarly journals Inventory and distribution of Oligochaeta (Annelida, Clitellata) in first-order streams in preserved areas of the state of Minas Gerais, Brazil

2013 ◽  
Vol 13 (1) ◽  
pp. 245-254 ◽  
Author(s):  
Luciana Falci Theza Rodrigues ◽  
Felipe Silveira Leite ◽  
Roberto da Gama Alves
Keyword(s):  
Minas Gerais ◽  
The State ◽  
Aquatic Environments ◽  
First Order ◽  
Number Of Species ◽  
First Occurrence ◽  
Lotic Environments ◽  
Shed Light

Data resulting from species inventories shed light on the richness and distribution of various groups. In Minas Gerais, work on inventory and distribution of the oligochaetes of lotic environments in preserved areas are non-existent. Therefore, this study aimed to inventory the limnic oligochaetes fauna of first-order streams located in four preserved areas, to expand knowledge of the ecology and distribution of this group. In total, 19 taxa were inventoried, belonging to the families Naididae and Enchytraeidae and the superorder Megadrili (earthworms), with the genus Pristina having the largest number of species. The number of species found in this investigation corresponds to 22% of oligochaetes species recorded in Brazilian aquatic environments. The results obtained add important knowledge of the distribution of some oligochaetes species in Brazil, represent the first records of species for the four preserved areas studied and confirm the first occurrence of various species in the state.

On the Operator Formulation of the Polyatomic Molecule Partition Function

1983 ◽  
Vol 38 (2) ◽  
pp. 167-183 ◽  
Author(s):  
J. Bohmann ◽  
W. Witschel
Keyword(s):  
Perturbation Theory ◽  
Partition Function ◽  
Polyatomic Molecule ◽  
Perturbation Series ◽  
Numerical Calculations ◽  
Model Systems ◽  
Coriolis Coupling ◽  
Commuting Operators ◽  
Operator Form ◽  
Statistical Perturbation

Abstract The Nielsen Hamiltonian of the general polyatomic molecule including anharmonicity and its resonances, Coriolis-coupling and its resonances, and rotation-vibration interaction are treated by statistical perturbation theory in its operator form. By generating function methods and operator theorems, which are treated in an appendix, cumbersome calculations with non-commuting operators are avoided. The results for H2O and SO2 agree very well with accurate numerical calculations from the literature. Qualitative conclusions on the convergence of the perturbation series are drawn from the numerical calculations for model systems.

scholarly journals FIELD THEORETIC CALCULATION OF SCALAR TURBULENCE

2001 ◽  
Vol 15 (26) ◽  
pp. 3419-3428 ◽  
Author(s):  
MAHENDRA K. VERMA
Keyword(s):  
Passive Scalar ◽  
Perturbation Series ◽  
Three Dimension ◽  
Higher Dimension ◽  
First Order ◽  
Scalar Turbulence ◽  
Flux Formula

The cascade rate of passive scalar and Bachelor's constant in scalar turbulence are calculated using the flux formula. This calculation is done to first order in perturbation series. Batchelor's constant in three dimension is found to be approximately 1.25. In higher dimension, the constant increases as d1/3.

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