{'fraction_non_alphanumeric': 0.02807486631016043, 'fraction_numerical': 0.008021390374331552, 'mean_word_length': 4.467153284671533, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Gravity in 2 + 1 dimensions as a Riemann - Hilbert problem

In this paper we consider (2 + 1)-dimensional gravity coupled to N point particles. We introduce a gauge in which the z and components of the dreibein field become holomorphic and anti-holomorphic, respectively. As a result we can restrict ourselves to the complex plane. Next we show that solving the dreibein field is equivalent to solving the Riemann - Hilbert problem for the group SO(2,1). We give the explicit solution for two particles in terms of hypergeometric functions. In the N-particle case we give a representation in terms of conformal field theory. The dreibeins are expressed as correlators of two free fermion fields and twist-operators at the position of the particles.