Papers by Daniel Jafferis
We propose that the three-dimensional N=2 SU(2) Chern-Simons theory at level 1 coupled to an adjo... more We propose that the three-dimensional N=2 SU(2) Chern-Simons theory at level 1 coupled to an adjoint chiral multiplet with no superpotential is equivalent to the free field theory consisting of a single massless N=2 chiral multiplet. In particular, we show that the two theories have the identical "Z-function" and identical superconformal index.
In four dimensional N=2 supergravity theories, BPS bound states near marginal stability are descr... more In four dimensional N=2 supergravity theories, BPS bound states near marginal stability are described by configurations of widely separated constituents with nearly parallel central charges. When the vacuum moduli can be dialed adiabatically until the central charges become anti -parallel, a paradox arises. We show that this paradox is always resolved by the existence of "bound state transformation walls" across
We compute the index of BPS states for two stacks of D4-branes wrapped on ample divisors and over... more We compute the index of BPS states for two stacks of D4-branes wrapped on ample divisors and overlapping over a compact Riemann surface inside non-compact Calabi-Yau 3-fold. This index is given in terms of U(N) x U(M) q-deformed Yang Mills theory with bifundamental matter. From the factorization in the limit of large D4 charge, we argue that our result computes
In this paper we study supersymmetric Chern-Simons-matter (CSM) theories with several Higgs branc... more In this paper we study supersymmetric Chern-Simons-matter (CSM) theories with several Higgs branches. Two such theories at small Chern-Simons level are conjectured to describe the superconformal field theory at the infrared fixed point of N = 4 QED with N_f = 2, 3. In particular, the mirror symmetry which exchanges the Coulomb and Higgs branches of N = 4 QED
Journal of High Energy Physics, 2008
We construct three dimensional Chern-Simons-matter theories with gauge groups U (N ) ×U (N ) and ... more We construct three dimensional Chern-Simons-matter theories with gauge groups U (N ) ×U (N ) and SU (N ) ×SU (N ) which have explicit N = 6 superconformal symmetry. Using brane constructions we argue that the U (N ) × U (N ) theory at level k describes the low energy limit of N M2-branes probing a C 4 /Z k singularity. At large N the theory is then dual to M-theory on AdS 4 × S 7 /Z k . The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS 4 × CP 3 . For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU (2) × SU (2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
We give an elementary physical derivation of the Kontsevich-Soibelman wall crossing formula, vali... more We give an elementary physical derivation of the Kontsevich-Soibelman wall crossing formula, valid for any theory with a 4d N = 2 supergravity description. Our argument leads to a slight generalization of the formula, which relates monodromy to the BPS spectrum.
Journal of High Energy Physics, 2008
We consider two generalizations of the N = 6 superconformal Chern-Simonsmatter theories with gaug... more We consider two generalizations of the N = 6 superconformal Chern-Simonsmatter theories with gauge group U (N ) × U (N ). The first generalization is to N = 6 superconformal U (M ) × U (N ) theories, and the second to N = 5 superconformal O(2M ) × U Sp(2N ) and O(2M + 1) × U Sp(2N ) theories. These theories are conjectured to describe M2-branes probing C 4 /Z k in the unitary case, and C 4 / D k in the orthogonal/symplectic case, together with a discrete flux, which can be interpreted as |M − N | fractional M2-branes localized at the orbifold singularity. The classical theories with these gauge groups have been constructed before; in this paper we focus on some quantum aspects of these theories, and on a detailed description of their M theory and type IIA string theory duals.
JHEP-Journal of High Energy Physics, 2008
We find the gravity duals to an infinite series of N = 3 Chern-Simons quiver theories. They are A... more We find the gravity duals to an infinite series of N = 3 Chern-Simons quiver theories. They are AdS 4 × M 7 vacua of M-theory, with M 7 in a certain class of 3-Sasaki-Einstein manifolds obtained by a quotient construction. The field theories can be engineered from a brane configuration; their geometry is summarized by a "hyperKähler toric fan" that can be read off easily from the relative angles of the branes. The singularity at the tip of the cone over M 7 is generically not an orbifold. The simplest new manifolds we consider can be written as the biquotient U(1)\U(3)/U(1). We also comment on the relation between our theories and four-dimensional N = 1 theories with the same quiver.
We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0... more We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kahler parameter of the rigid sphere it is necessary to introduce an extra real parameter to describe BPS partition functions and marginal stability walls. The supergravity approach to BPS state-counting gives a
We compute the index of BPS states for two stacks of D4-branes wrapped on ample divisors and over... more We compute the index of BPS states for two stacks of D4-branes wrapped on ample divisors and overlapping over a compact Riemann surface inside non-compact Calabi-Yau 3-fold. This index is given in terms of U(N) x U(M) q-deformed Yang Mills theory with bifundamental matter. From the factorization in the limit of large D4 charge, we argue that our result computes the jump in the index of BPS states across the wall of the marginal stability for the split flow of a D4 brane fragmenting into a pair of D4 branes.
Journal of High Energy Physics, 2006
We develop means of computing exact degerenacies of BPS black holes on toric Calabi-Yau manifolds... more We develop means of computing exact degerenacies of BPS black holes on toric Calabi-Yau manifolds. We show that the gauge theory on the D4 branes wrapping ample divisors reduces to 2D q-deformed Yang-Mills theory on necklaces of P 1 's. As explicit examples we consider local P 2 , P 1 × P 1 and A k type ALE space times C. At large N the D-brane partition function factorizes as a sum over squares of chiral blocks, the leading one of which is the topological closed string amplitude on the Calabi-Yau. This is in complete agreement with the recent conjecture of Ooguri, Strominger and Vafa. December, 2005
Journal of High Energy Physics, 2011
For 3-dimensional field theories with N = 2 supersymmetry the Euclidean path integrals on the thr... more For 3-dimensional field theories with N = 2 supersymmetry the Euclidean path integrals on the three-sphere can be calculated using the method of localization; they reduce to certain matrix integrals that depend on the R-charges of the matter fields. We solve a number of such large N matrix models and calculate the free energy F as a function of the trial R-charges consistent with the marginality of the superpotential. In all our N = 2 superconformal examples, the local maximization of F yields answers that scale as N 3/2 and agree with the dual M-theory backgrounds AdS 4 × Y , where Y are 7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local F -maximization is equivalent to the minimization of the volume of Y over the space of Sasakian metrics, a procedure also referred to as Z-minimization. Moreover, we find that the functions F and Z are related for any trial R-charges. In the models we study F is positive and decreases along RG flows. We therefore propose the "F -theorem" that we hope applies to all 3-d field theories: the finite part of the free energy on the three-sphere decreases along RG trajectories and is stationary at RG fixed points. We also show that in an infinite class of Chern-Simons-matter gauge theories 7.3.4 Q 1,1,1
Journal of High Energy Physics, 2012
In four dimensional N=2 supergravity theories, BPS bound states near marginal stability are descr... more In four dimensional N=2 supergravity theories, BPS bound states near marginal stability are described by configurations of widely separated constituents with nearly parallel central charges. When the vacuum moduli can be dialed adiabatically until the central charges become anti -parallel, a paradox arises. We show that this paradox is always resolved by the existence of "bound state transformation walls" across which the nature of the bound state changes, although the index does not jump. We find that there are two distinct phenomena that can take place on these walls, which we call recombination and conjugation. The latter is associated to the presence of singularities at finite distance in moduli space. Consistency of conjugation and wall-crossing rules near these singularities leads to new constraints on the BPS spectrum. Singular loci supporting massless vector bosons are particularly subtle in this respect. We argue that the spectrum at such loci necessarily contains massless magnetic monopoles, and that bound states around them transform by intricate hybrids of conjugation and recombination.
Communications in Mathematical Physics, 2009
In this paper we study the relation between pyramid partitions with a general empty room configur... more In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kähler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers.
Journal of High Energy Physics, 2010
Understanding the strong coupling limit of massive type IIA string theory is a longstanding probl... more Understanding the strong coupling limit of massive type IIA string theory is a longstanding problem. We argue that perhaps this problem does not exist; namely, there may be no strongly coupled solutions of the massive theory. We show explicitly that massive type IIA string theory can never be strongly coupled in a weakly curved region of space-time. We illustrate our general claim with two classes of massive solutions in AdS 4 × CP 3 : one, previously known, with N = 1 supersymmetry, and a new one with N = 2 supersymmetry. Both solutions are dual to d = 3 Chern-Simons-matter theories. In both these massive examples, as the rank N of the gauge group is increased, the dilaton initially increases in the same way as in the corresponding massless case; before it can reach the M-theory regime, however, it enters a second regime, in which the dilaton decreases even as N increases. In the N = 2 case, we find supersymmetry-preserving gauge-invariant monopole operators whose mass is independent of N . This predicts the existence of branes which stay light even when the dilaton decreases. We show that, on the gravity side, these states originate from D2-D0 bound states wrapping the vanishing two-cycle of a conifold singularity that develops at large N .
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Papers by Daniel Jafferis