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In this note, we show that the potential vector field of a Cotton soliton (M, g, V) is an infinitesimal harmonic transformation, and we use it to give another proof of the triviality of compact Cotton solitons. Moreover, we extend this triviality result to the complete case by imposing certain regularity conditions on the potential vector field V. [ABSTRACT FROM AUTHOR]

We study an almost Yamabe soliton (Mn, g, V, ρ) and obtain various conditions on V in terms of infinitesimal harmonic transformation, 2-Killing, and an inequality, to show that V is Killing. In addition, we have provided characterizations of a 2-Killing vector field V on any Riemannian manifold in terms of the strain tensor and divergence of V. [ABSTRACT FROM AUTHOR]

We provide a direct proof of the result “A closed Yamabe soliton of dimension ≥ 3 has constant scalar curvature” through the derivation of a divergence formula. Next, we show that, if the potential vector field of a Yamabe soliton of dimension ≥ 3 leaves the Ricci tensor invariant, then the scalar curvature is constant. Finally, we provide a classification of a complete non-trivial gradient Kähler Yamabe soliton, showing that it is isometric to either (i) a product of a complex Euclidean space and a Kähler manifold of non-zero constant scalar curvature, or (ii) a complex Euclidean space. [ABSTRACT FROM AUTHOR]

We derive a divergence formula for an m-quasi Yamabe gradient soliton with finite m, and use it to give a short proof of the result "A compact m-quasi Yamabe gradient soliton (M n , g) , n ≥ 3 , with finite m, has constant scalar curvature". We also show that an m-quasi Yamabe gradient soliton with finite m and positive scalar curvature, whose soliton vector field leaves the Ricci tensor invariant, is shrinking and has constant scalar curvature. [ABSTRACT FROM AUTHOR]

Flat space cosmologies (FSCs) are time dependent solutions of three-dimensional (3D) gravity with a vanishing cosmological constant. They can be constructed from a discrete quotient of empty 3D flat spacetime and are also called shifted-boost orbifolds. Using this quotient structure, we build a new and generalized Selberg zeta function for FSCs, and show that it is directly related to the scalar 1-loop partition function. We then propose an extension of this formalism applicable to more general quotient manifolds M /ℤ, based on representation theory of fields propagating on this background. Our prescription constitutes a novel and expedient method for calculating regularized 1-loop determinants, without resorting to the heat kernel. We compute quasinormal modes in the FSC using the zeroes of a Selberg zeta function, and match them to known results. [ABSTRACT FROM AUTHOR]

We study a nearly Kaehler manifold M admitting a closed conformal vector field V, and obtain three results under the following assumptions (i) V is almost analytic, (ii) M has real dimension > 6 , is complete and strictly nearly Kaehler, and (iii) M is complete strictly nearly Kaehler of global constant type. [ABSTRACT FROM AUTHOR]

We study a complete connected generalized m-quasi-Einstein manifold M with finite m, admitting a non-homothetic, non-parallel, complete closed conformal vector field V, and show that either M is isometric to a round sphere, or the Ricci tensor can be expressed explicitly in terms of the conformal data over an open dense subset. In the latter case, we prove that M is a warped product of an open real interval with an Einstein manifold; furthermore, it is conformally flat in dimension 4 and has vanishing Cotton and Bach tensors in dimension > 3. Next, we obtain the same explicit expression for the Ricci tensor, and analogous results, for a gradient Ricci almost soliton endowed with a non-parallel closed conformal vector field. [ABSTRACT FROM AUTHOR]

We study a non-trivial radially flat generalized m-quasi Einstein manifold M with finite m and Codazzi Ricci tensor, and obtain an explicit expression of the Ricci tensor over an open dense subset M ∗ of M on which the gradient of the potential function vanishes nowhere. Further, we prove that M ∗ is either Ricci-flat or is a non-steady m-quasi Einstein manifold which is locally a product of a line and an (n - 1) -dimensional Einstein space. In both the cases, M ∗ is conformally flat in dimension 4, and the Bach tensor vanishes in any dimension ≥ 3 . Finally, we show that an m-quasi Einstein manifold with m ≠ 1 (finite) and constant scalar curvature admitting a non-parallel closed conformal vector field is Einstein. [ABSTRACT FROM AUTHOR]

It is shown that the scalar curvature of a Yamabe soliton as a Sasakian manifold is constant and the soliton vector field is Killing. The same conclusion is shown to hold for a Yamabe soliton as a K-contact manifold M2n+1 if any one of the following conditions hold: (i) its scalar curvature is constant along the soliton vector field V, (ii) V is an eigenvector of the Ricci operator with eigenvalue 2n, (iii) V is gradient. [ABSTRACT FROM AUTHOR]

The Selberg zeta function and trace formula are powerful tools used to calculate kinetic operator spectra and quasinormal modes on hyperbolic quotient spacetimes. In this article, we extend this formalism to non-hyperbolic quotients by constructing a Selberg zeta function for warped AdS3 black holes. We also consider the so-called self-dual solutions, which are of interest in connection to near-horizon extremal Kerr. We establish a map between the zeta function zeroes and the quasinormal modes on warped AdS3 black hole backgrounds. In the process, we use a method involving conformal coordinates and the symmetry structure of the scalar Laplacian to construct a warped version of the hyperbolic half-space metric, which to our knowledge is new and may have interesting applications of its own, which we describe. We end by discussing several future directions for this work, such as computing 1-loop determinants (which govern quantum corrections) on the quotient spacetimes we consider, as well as adapting the formalism presented here to more generic orbifolds. [ABSTRACT FROM AUTHOR]

The two-character level-1 WZW models corresponding to Lie algebras in the Cvitanović-Deligne series A1, A2, G2, D4, F4, E6, E7 have been argued to form coset pairs with respect to the meromorphic E8,1 CFT. Evidence for this has taken the form of holomorphic bilinear relations between the characters. We propose that suitable 4-point functions of primaries in these models also obey bilinear relations that combine them into current correlators for E8,1, and provide strong evidence that these relations hold in each case. Different cases work out due to special identities involving tensor invariants of the algebra or hypergeometric functions. In particular these results verify previous calculations of correlators for exceptional WZW models, which have rather subtle features. We also find evidence that the intermediate vertex operator algebras A0.5 and E7.5, as well as the three-character A4,1 theory, also appear to satisfy the novel coset relation. [ABSTRACT FROM AUTHOR]

Quasi-characters are vector-valued modular functions having an integral, but not necessarily positive, q-expansion. Using modular differential equations, a complete classification has been provided in arXiv:1810.09472 for the case of two characters. These in turn generate all possible admissible characters, of arbitrary Wronskian index, in order two. Here we initiate a study of the three-character case. We conjecture several infinite families of quasi-characters and show in examples that their linear combinations can generate admissible characters with arbitrarily large Wronskian index. The structure is completely different from the order two case, and the novel coset construction of arXiv:1602.01022 plays a key role in discovering the appropriate families. Using even unimodular lattices, we construct some explicit three-character CFT corresponding to the new admissible characters. [ABSTRACT FROM AUTHOR]

We investigate a conjecture to describe the characters of large families of RCFT's in terms of contour integrals of Feigin-Fuchs type. We provide a simple algorithm to determine the modular S -matrix for arbitrary numbers of characters as a sum over paths. Thereafter we focus on the case of 2, 3 and 4 characters, where agreement between the critical exponents of the integrals and the characters implies that the conjecture is true. In these cases, we compute the modular S-matrix explicitly, verify that it agrees with expectations for known theories, and use it to compute degeneracies and multiplicities of primaries. We verify that our algorithm reproduces the correct S -matrix for SU (2)k for all k ≤ 18 which provides additional evidence for the original conjecture. On the way we note that the Verlinde formula provides interesting constraints on the critical exponents of RCFT in this context. [ABSTRACT FROM AUTHOR]