John Kehayias (Vanderbilt University)
We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu-Goldstone boson (NGB) of a nonlinear sigma model (NLSM). However, it is well known that NLSMs with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry --- making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space $SU(3)/SU(2)×U(1)$, with the Higgs as the NGB. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten-Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion.