Conformal QED_d,F-theorem and theϵexpansion

Author name not available (Why is that?)

Abstract: We calculate the free energies

F

for

U (1)

gauge theories on the

d

dimensional sphere of radius

R

. For the theory with free Maxwell action we find the exact result as a function of

d

; it contains the term

f r a c d - 4 2 l o g R

consistent with the lack of conformal invariance in dimensions other than 4. When the

U (1)

gauge theory is coupled to a sufficient number

N_{f}

of massless 4 component fermions, it acquires an interacting conformal phase, which in

d < 4

describes the long distance behavior of the model. The conformal phase can be studied using large

N_{f}

methods. Generalizing the

d = 3

calculation in arXiv:1112.5342, we compute its sphere free energy as a function of

d

, ignoring the terms of order

1 / N_{f}

and higher. For finite

N_{f}

, following arXiv:1409.1937 and arXiv:1507.01960, we develop the

4 - e p s i l o n

expansion for the sphere free energy of conformal QED

_{d}

. Its extrapolation to

d = 3

shows very good agreement with the large

N_{f}

approximation for

N_{f} > 3

. For

N_{f}

at or below some critical value

N_{m c r i t}

, the

S U (2 N_{f})

symmetric conformal phase of QED

_{3}

is expected to disappear or become unstable. By using the

F

-theorem and comparing the sphere free energies in the conformal and broken symmetry phases, we show that

N_{m c r i t} l e q 4

. As another application of our results, we calculate the one loop beta function in conformal QED

_{6}

, where the gauge field has a 4-derivative kinetic term. We show that this theory coupled to

N_{f}

massless fermions is asymptotically free.

No records found.

No records found.

This page was built for publication: Conformal QED_d,F-theorem and theϵexpansion

Conformal QEDd,F-theorem and theϵexpansion