Synopsis: When Symmetries Conform to Theories

Theorists gain insight into mechanisms that enhance the available symmetries of various quantum field theories.
Synopsis figure
D. M. Hofman and A. Strominger, Phys. Rev. Lett. (2011)

The study of conformal field theories—quantum field theories, generally defined in two dimensions, invariant under conformal transformations (loosely “shape-preserving”) of spacetime—is the cornerstone of fields as diverse as critical phenomena, black holes, and string theory. There is, by now, a large body of literature devoted to the extraction of detailed physical properties of such conformal field theories based on powerful algebraic methods. The key reason behind the solvability of conformal field theories is that the conformal invariance in two spacetime dimensions implies an infinite number of symmetries, thus severely restricting the physical properties of the theories for which conformal transformations are a preserved symmetry. However, an interesting converse question may be asked. Given a two-dimensional field theory, invariant under a finite number of symmetries, under what conditions can one expect the dynamical system to be conformally invariant?

Writing in Physical Review Letters, Diego Hofman and Andrew Strominger from Harvard University study and partially answer this question. The authors show that given a two-dimensional theory with translational and partial scale invariance—a rather minimal set of assumptions—the requirements of locality, unitarity, and a positive spectrum force the field theory to have an infinite number of additional symmetries. The added symmetries are conformal transformations and generalizations thereof. This powerful conclusion, obtained about a large class of models, is expected to be relevant to diverse areas of physics research, in particular, to the applications of the gauge-gravity duality in condensed matter physics. – Abhishek Agarwal


More Announcements »

Subject Areas

Particles and Fields

Previous Synopsis


Circuit Analysis

Read More »

Next Synopsis

Related Articles

Viewpoint: Ghostly Neutrino Comes into Sharper Focus
Particles and Fields

Viewpoint: Ghostly Neutrino Comes into Sharper Focus

The first results from the NOvA experiment set new constraints on charge-parity violation in neutrinos and on the ordering of neutrino masses. Read More »

Synopsis: Explaining a 750  GeV Bump
Particles and Fields

Synopsis: Explaining a 750 GeV Bump

Theorists try to explain data from the LHC that could be hinting at the existence of new particles. Read More »

Synopsis: The Heavy Limit of Dark Matter
Particles and Fields

Synopsis: The Heavy Limit of Dark Matter

A theoretical investigation of super-heavy dark matter particles finds that their existence might be discerned in the cosmic microwave background. Read More »

More Articles