Abstract
We systematically analyze the effective action on the moduli space of (2, 0) superconformal field theories in six dimensions, as well as their toroidal compactification to maximally supersymmetric Yang-Mills theories in five and four dimensions. We present a streamlined approach to non-renormalization theorems that constrain this effective action. The first several orders in its derivative expansion are determined by a one-loop calculation in five-dimensional Yang-Mills theory. This fixes the leading higher-derivative operators that describe the renormalization group flow into theories residing at singular points on the moduli space of the compactified (2, 0) theories. This understanding allows us to compute the a-type Weyl anomaly for all (2, 0) superconformal theories. We show that it decreases along every renormalization group flow that preserves (2, 0) supersymmetry, thereby establishing the a-theorem for this class of theories. Along the way, we encounter various field-theoretic arguments for the ADE classification of (2, 0) theories.
Highlights
Maximal supersymmetry.1 This allows us to show that the functional form of the effective action at the first several orders in the derivative expansion is completely fixed in terms of a few coefficients
This fixes the leading higher-derivative operators that describe the renormalization group flow into theories residing at singular points on the moduli space of the compactified (2, 0) theories. This understanding allows us to compute the a-type Weyl anomaly for all (2, 0) superconformal theories. We show that it decreases along every renormalization group flow that preserves (2, 0) supersymmetry, thereby establishing the a-theorem for this class of theories
We show that the a-anomaly is strictly decreasing under all renormalization group (RG) flows that preserve (2, 0) supersymmetry, verifying the conjectured a-theorem [9] in six dimensions for this class of flows
Summary
Anomalies are robust observables: even in a strongly-coupled theory, they can often be computed by utilizing different effective descriptions, some of which may be weakly coupled. By analogy with N = 4 Yang-Mills theory in four dimensions, where a WZ term is generated at one loop on the Coulomb branch [30], one might expect that ∆k only depends on nW = dg − (dh + 1), the number of W-Bosons that become massive upon breaking g → h ⊕ u(1). By compactifying the theory on T 2 and tracking this four-derivative term as the torus shrinks to zero size, they argued that b could be extracted from a one-loop computation in four-dimensional N = 4 Yang-Mills theory with gauge algebra g This leads to b ∼ nW , the number of massive W-Bosons. This puzzle will be resolved in the course of our investigation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
