Abstract
Via large and small $N_c$ relations we derive nonperturbative results about the conformal window of two-index theories. Using Schwinger-Dyson methods as well as four-loops results we estimate subleading corrections and show that naive large number of colors extrapolations are unreliable when $N_c$ is less than about six. Nevertheless useful nonperturbative inequalities for the size of the conformal windows, for any number of colors, can be derived. By further observing that the adjoint conformal window is independent of the number of colors we argue, among other things, that: The large $N_c$ two-index conformal window is twice the conformal window of the adjoint representation (which can be determined at small $N_c$) expressed in terms of Dirac fermions; Lattice results for adjoint matter can be used to provide independent information on the conformal dynamics of two-index theories such as SU($N_c$) with two and four symmetric Dirac flavors.
Highlights
JHEP12(2015)054 constrain the size of two-index conformal windows
By further observing that the adjoint conformal window is independent of the number of colors we argue, among other things, that: the large Nc two-index conformal window is twice the conformal window of the adjoint representation expressed in terms of Dirac fermions; lattice results for adjoint matter can be used to provide independent information on the conformal dynamics of two-index theories such as SU(Nc) with two and four symmetric Dirac flavors
In the large Nc limit the number of degrees of freedom equal Nc2 in all three cases and the theory with Nwf [G] adjoint Weyl fermions is equivalent to the theory with Nf [S2/A2] Dirac fermions in either the two-index symmetric or two-index antisymmetric representation
Summary
JHEP12(2015)054 constrain the size of two-index conformal windows. By further noting the Nc independence of the adjoint conformal window we will argue that: the large Nc conformal window of two-index theories is twice the conformal window of the adjoint representation in terms of Dirac fermions; lattice results, obtained at small Nc, for adjoint matter can be used to cross check and predict the conformal dynamics of two-index theories at large and small number of colors. By further observing that the adjoint conformal window is independent of the number of colors we argue, among other things, that: the large Nc two-index conformal window is twice the conformal window of the adjoint representation (which can be determined at small Nc) expressed in terms of Dirac fermions; lattice results for adjoint matter can be used to provide independent information on the conformal dynamics of two-index theories such as SU(Nc) with two and four symmetric Dirac flavors.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have