Does string theory provide a physical regulator for Standard Model divergencies? - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-09-21T09:31:53Z https://physics.stackexchange.com/feeds/question/36387 https://creativecommons.org/licenses/by-sa/4.0/rdf https://physics.stackexchange.com/q/36387 11 Does string theory provide a physical regulator for Standard Model divergencies? Diego Mazón https://physics.stackexchange.com/users/10522 2012-09-14T06:02:23Z 2012-09-14T07:53:31Z <p>In other question, Ron Maimon says that he thinks string theory is the <em>physical</em> regulator. I did not know that string theory regularize divergencies.</p> <p>So, <strong>Q1</strong>: How does string theory regularize the ultra-violet divergencies of the "low-energy" (Standard Model) fields? And <strong>Q2</strong>: Why it doesn't regularize its own divergencies.</p> <p>By regularization I mean that the theory is ultra-violet finite before removing the regulator. </p> https://physics.stackexchange.com/questions/36387/-/36389#36389 12 Answer by Luboš Motl for Does string theory provide a physical regulator for Standard Model divergencies? Luboš Motl https://physics.stackexchange.com/users/1236 2012-09-14T07:10:01Z 2012-09-14T07:10:01Z <p>The answer to both questions is that string theory is completely free of any ultraviolet divergences. It follows that its effective low-energy descriptions such as the Standard Model automatically come with a regulator.</p> <p>An important "technicality" to notice is that the formulae for amplitudes in string theory are not given by the same integrals over loop momenta as in quantum field theory. Instead, the Feynman diagrams in string theory are Riemann surfaces, world sheets, and one integrates over their possible conformal shapes (moduli).</p> <p>Nevertheless, if one rewrites these integrals in a way that is convenient to extract the low-energy limit of string theory, one may see that the stringy diagrams boil down to the quantum field theory diagrams at low energies and the formulae are the same except for modifications that become large, $O(1)$, at energies of order $m_{\rm string}\sim \sqrt{T}$. The string scale is where perturbative string theory's corrections to quantum field theory become substantial and that's where the typical power-law increasing divergences in QFT are replaced by the exponentially decreasing, ultra-soft stringy behavior.</p> <p>The reason/proof why/that string theory has no UV divergences has been known for decades. UV divergences would arise from extreme corners of the moduli space of Riemann surfaces in which the "length of various tubes" inside the degenerating Riemann surface would go to zero. But all such extreme diagrams are equivalent to diagrams with "extremely thin tubes" and may therefore be reinterpreted as IR divergences: it's the only right interpretation of these divergences and no "extra UV divergences" exist because it would be double-counting.</p> <p>Bosonic string theory has infrared divergences due to the tachyon and dilaton and their long-range effects. However, in 10-dimensional superstring theory, one may prove that all the IR divergences – and there are just several a priori possible candidates that could be nonzero to start with – cancel, essentially due to supersymmetry. It follows that superstring theory is free of all divergences.</p>