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A loophole in the proofs of asymptotic freedom and quantum triviality
Paul Romatschke
In 1973, Coleman and Gross proved that in four dimensions, only non-abelian gauge theories can have asymptotic freedom. More recently, Aizenman and Duminil-Copin proved that four d…
Negative Coupling on the Lattice
Paul Romatschke
Triviality of theory in four dimensions can be avoided if the bare coupling constant is negative in the UV. Theories with negative coupling can be put on the lattice if the i…
Vanishing Polyakov Loop for QCD with Twelve Massless Quarks
Seth Grable, Paul Romatschke
We consider continuum-formulation QCD in four dimensions with twelve massless fundamental quark flavors. Splitting the SU(\(N\)) gauge field into background and fluctuation parts,…
Quantum Field Theory in Large N Wonderland: Three Lectures
Paul Romatschke
In these lecture notes, I review how to use large N techniques to solve quantum field theories in various dimensions. In particular, the case of N-dimensional quantum mechanics, no…
What if theory in 4 dimensions is non-trivial in the continuum?
Paul Romatschke
Traditionally, scalar theory in four dimensions is thought to be quantum trivial in the continuum. This tradition is apparently well grounded both in physics arguments and ma…
Instantons, analytic continuation, and -symmetric field theory
Scott Lawrence, Christian Peterson, Paul Romatschke +1
Ordinary Hermitian theory is known to exist in dimensions when . For negative values of the coupling, it has been suggested that a physical meaningful definition…