Non-perturbative formulas for central functions of supersymmetric gauge theories

Anselmi, Damiano; Freedman, Daniel Z.; Grisaru, Marcus T.; Johansen, A.

doi:10.1016/s0550-3213(98)00278-8

Cited by 427 publications

(707 citation statements)

References 25 publications

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“…We can thus trust the relations of [8,9]      c = 3 32 3 trR 3 − trR a = 3 32 3 trR 3 − 5 trR (2.13)…”

Section: Jhep04(2006)032mentioning

confidence: 73%

“…In [8,9] exact formulae relating the gravitational central charges to the 't Hooft anomalies of the R-current have been found:…”

Section: Superconformal Quiver Implies C = Amentioning

confidence: 99%

“…Now we have to reconstruct the three block quivers, starting from the four triples of Table 2. This is a bit long but straightforward, so we discuss just the more involved example: (X, Y, Z) = (8,8,16). This is precisely the case where we find quivers not directly related to del Pezzo surfaces.…”

Section: Jhep04(2006)032mentioning

confidence: 99%

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New results on superconformal quivers

Benvenuti¹,

Hanany²

2006

J. High Energy Phys.

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All superconformal quivers are shown to satisfy the relation c = a and are thus good candidates for being the field theory living on D3 branes probing CY singularities. We systematically study 3 block and 4 block chiral quivers which admit a superconformal fixed point of the RG equation. Most of these theories are known to arise as living on D3 branes at a singular CY manifold, namely complex cones over del Pezzo surfaces. In the process we find a procedure of getting a new superconformal quiver from a known one. This procedure is termed "shrinking" and, in the 3 block case, leads to the discovery of two new models. Thus, the number of superconformal 3 block quivers is 16 rather than the previously known 14. We prove that this list exausts all the possibilities. We suggest that all rank 2 chiral quivers are either del Pezzo quivers or can be obtained by shrinking a del Pezzo quiver and verify this statement for all 4 block quivers, where a lot of "shrunk" del Pezzo models exist.

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“…We can thus trust the relations of [8,9]      c = 3 32 3 trR 3 − trR a = 3 32 3 trR 3 − 5 trR (2.13)…”

Section: Jhep04(2006)032mentioning

confidence: 73%

“…In [8,9] exact formulae relating the gravitational central charges to the 't Hooft anomalies of the R-current have been found:…”

Section: Superconformal Quiver Implies C = Amentioning

confidence: 99%

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New results on superconformal quivers

Benvenuti¹,

Hanany²

2006

J. High Energy Phys.

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“…It is further conjectured [7], with much supporting evidence e.g. [8,9,10,11], that an appropriate such central charge (at least at RG fixed points) is the coefficient 2 "a" of a 1 Non-asymptotically free theories, on the other hand, flow to free field theories in the IR (at least when one starts the RG flow at weak coupling).…”

Section: Introductionmentioning

confidence: 94%

RG fixed points and flows in SQCD with adjoints

2004

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We map out and explore the zoo of possible 4d N = 1 superconformal theories which are obtained as RG fixed points of N = 1 SQCD with N f fundamental and N a adjoint matter representations. Using "a-maximization," we obtain exact operator dimensions at all RG fixed points and classify all relevant, Landau-Ginzburg type, adjoint superpotential deformations. Such deformations can be used to RG flow to new SCFTs, which are then similarly analyzed. Remarkably, the resulting 4d SCFT classification coincides with Arnold's ADE singularity classification. The exact superconformal R-charge and the central charge a are computed for all of these theories. RG flows between the different fixed points are analyzed, and all flows are verified to be compatible with the conjectured a-theorem.

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“…If R µ denotes the R-symmetry current, then the anomaly coefficients a and c are related to the U (1) R -gravitational and U (1) 3 R anomalies [18],…”

Section: Hmentioning

confidence: 99%

Toric duality is Seiberg duality

Beasley¹,

Plesser²

2001

J. High Energy Phys.

147

258

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We study four N = 1 SU (N ) 6 gauge theories, with bi-fundamental chiral matter and a superpotential. In the infrared, these gauge theories all realize the low-energy worldvolume description of N coincident D3-branes transverse to the complex cone over a del Pezzo surface dP 3 which is the blowup of P 2 at three generic points. Therefore, the four gauge theories are expected to fall into the same universality class-an example of a phenomenon that has been termed "toric duality." However, little independent evidence has been given that such theories are infrared-equivalent.In fact, we show that the four gauge theories are related by the N = 1 duality of Seiberg, vindicating this expectation. We also study holographic aspects of these gauge theories. In particular we relate the spectrum of chiral operators in the gauge theories to wrapped D3-brane states in the AdS dual description. We finally demonstrate that the other known examples of toric duality are related by N = 1 duality, a fact which we conjecture holds generally.

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Non-perturbative formulas for central functions of supersymmetric gauge theories

Cited by 427 publications

References 25 publications

New results on superconformal quivers

New results on superconformal quivers

RG fixed points and flows in SQCD with adjoints

Toric duality is Seiberg duality

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