Gauge theory in de Sitter space-time from a holographic model

Abstract

Yang-Mills (YM) theory with flavor quarks in the ${\mathrm{dS}}_{4}$ is studied through the dual supergravity in the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ background with nontrivial dilaton and axion. The flavor quarks are introduced by embedding a probe D7 brane. We find that the dynamical properties of YM theory in the ${\mathrm{dS}}_{4}$ are similar to the case of the finite temperature theory given by the 5d AdS-Schwarzschild background. In the case of ${\mathrm{dS}}_{4}$, however, contrary to the finite temperature case, the gauge-field condensate plays an important role on the dynamical properties of quarks. We also give the quark-antiquark potential and meson spectra to find possible quark-bound states. We arrive at the conclusion that, while the quarks are not confined in the ${\mathrm{dS}}_{4}$, we could find stable meson states at very small cosmological constant as expected in the present universe. However, there would be no hadrons at early universe as in the inflation era.