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Thus the question is: Does the existence of tachyons make the theory inconsistent? Or does it simply indicate that we are quantizing the theory around the wrong point? The problem in analyzing this question stems from the fact that unlike the example in a scalar ﬁeld theory, the tachyon in string theory does not obviously come from quantization of a scalar ﬁeld. Thus in order to understand the tachyon, we have to reconstruct the scalar ﬁeld and its potential from the known results in string theory, and then analyze if the potential has a minimum.

Ross Ann. Henri Poincar´e [15] P. Horava and E. Witten, Nucl. Phys. B 475, 94 (1995) ; P. Horava, Phys. Rev. D 54, 7561 (1996). [16] E. Witten, Nucl. Phys. B 471, 135 (1996). [17] N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett. B 429, 263 (1998); Phys. Rev. ; I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G. Dvali, Phys. Lett B 426, 257 (1998). G. K. and Theory Group CERN 1211 Geneva 23 Switzerland Ann. Henri Poincar´e 4, Suppl. 1007/s00023-003-0904-3 Annales Henri Poincar´ e Tachyons in String Theory Ashoke Sen Abstract.

Thus, in contrast to approaches developed by particle physicists, one does not begin with quantum matter on a background geometry and use perturbation theory to incorporate quantum eﬀects of gravity. 1 In classical gravity, Riemannian geometry provides the appropriate mathematical language to formulate the physical, kinematical notions as well as the ﬁnal dynamical equations. This role is now taken by quantum Riemannian geometry, discussed below. In the classical domain, general relativity stands out as the best available theory of gravity, some of whose predictions have been tested to an amazing accuracy, surpassing even the legendary tests of quantum electrodynamics.