Central charges from the (N)=1 superconformal index.
Arash Arabi Ardehali1, James T Liu1, Phillip Szepietowski2
1Michigan Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA.
Physical Review Letters
|March 21, 2015
Summary
We developed methods to calculate central charges (a and c) in superconformal quantum field theories using the superconformal index. These findings apply to both holographic and non-holographic theories, extending beyond the large-N limit.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- String Theory
Background:
- Superconformal quantum field theories (SCFTs) are crucial in understanding quantum gravity and condensed matter systems.
- Central charges (a and c) characterize the conformal anomaly and play a vital role in renormalization group flow.
- The superconformal index offers a powerful, computable quantity for studying SCFTs.
Purpose of the Study:
- To derive novel prescriptions for calculating the central charges (a and c) of four-dimensional SCFTs.
- To investigate the relationship between the superconformal index and central charges in holographic and non-holographic contexts.
- To verify the exact AdS/CFT correspondence for specific classes of theories.
Main Methods:
- Utilizing the superconformal index as a computational tool.
- Applying derived prescriptions to holographic theories dual to Sasaki-Einstein 5-manifolds.
- Analyzing toric quiver CFTs without adjoint matter.
- Extending the analysis to non-holographic theories and away from the large-N limit.
Main Results:
- Prescriptions for obtaining central charges a and c from the superconformal index are presented.
- For holographic theories at infinite N, these prescriptions yield the O(1) parts of the central charges.
- Exact matching of central charges a and c is demonstrated for arbitrary toric quiver CFTs dual to smooth Sasaki-Einstein 5-manifolds.
- Evidence supporting the applicability of these results to non-holographic theories and beyond the large-N limit is provided.
Conclusions:
- The superconformal index provides a direct route to calculating central charges in SCFTs.
- The study confirms precise AdS/CFT matching for a broad class of holographic theories.
- The presented methods offer a versatile framework applicable to diverse theoretical physics settings.
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