Abstract
We extend and refine recent results on Renyi entropy in two-dimensional conformal field theories at large central charge. To do so, we examine the effects of higher spin symmetry and of allowing unequal left and right central charges, at leading and subleading order in large total central charge. The result is a straightforward generalization of previously derived formulae, supported by both gravity and CFT arguments. The preceding statements pertain to CFTs in the ground state, or on a circle at unequal left- and right-moving temperatures. For the case of two short intervals in a CFT ground state, we derive certain universal contributions to Renyi and entanglement entropy from Virasoro primaries of arbitrary scaling weights, to leading and next-to-leading order in the interval size; this result applies to any CFT. When these primaries are higher spin currents, such terms are placed in one-to-one correspondence with terms in the bulk 1-loop determinants for higher spin gauge fields propagating on handlebody geometries.
Highlights
Two-dimensional conformal field theories are among the most well-understood quantum field theories
We extend and refine recent results on Renyi entropy in two-dimensional conformal field theories at large central charge
We find an unsurprising universality: at large central charge in a spatially compact CFT with TL = TR, the finite size of the circle is invisible in the leading approximation to the single interval entanglement entropy
Summary
Two-dimensional conformal field theories are among the most well-understood quantum field theories. The universal dynamics of the current sector of such theories at large cL + cR is described by topologically massive gravity (TMG) [14, 15], another fairly exotic theory This time, we find that at leading order in large cL + cR, the Renyi entropy only reflects the gravitational anomaly [16] for chirally asymmetric states, such as a spatially compact CFT with unequal left- and right-moving temperatures. For the higher spin case, we will focus on the Renyi entropy of two intervals in the ground state, and explicitly compute corrections at next-to-leading order in large c = cL = cR Working in both CFT and gravity, our methodology is as follows. The day this work appeared on the arXiv, so did [23], which overlaps with sections 4 and 5 below
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