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On Modified Gravity
We consider some aspects of nonlocal modified gravity, where nonlocality is
of the type . In particular, using ansatz of the form
we find a few solutions for the spatially flat
FLRW metric. There are singular and nonsingular bounce solutions. For late
cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is
decelerated. R (t) = 0 satisfies all equations when k = -1.Comment: added references; made some clarifications; 8 page
Aspects of WZW models at critical level
We consider non-compact WZW models at critical level (equal to the dual
Coxeter number) as tensionless limits of gravitational backgrounds in string
theory. Special emphasis is placed on the Euclidean black hole coset
SL(2,R)_k/U(1) when k=2. In this limit gravity decouples in the form of a
Liouville field with infinite background charge and the world-sheet symmetry of
the model becomes a truncated version of W_\infty without Virasoro generator.
This is regarded as manifestation of Langlands duality for the SL(2,R)_k
current algebra that relates small with large values of the level in the two
extreme limits. However, the physical interpretation of the SL(2,R)_k/U(1)
coset model below the self-dual value k=3 remains elusive including the
non-conformal theory at k=2.Comment: 11 pages, contribution to the proceedings of 37th International
Symposium Ahrenshoop (Berlin, 2004
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