Diego M. Hofman

Bio: Diego M. Hofman is an academic researcher from Princeton University. The author has contributed to research in topics: Magnon & Graviton. The author has an hindex of 3, co-authored 3 publications receiving 1074 citations.

Giant Magnons

Abstract: Studies of ${\cal N}=4$ super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain These spin chains have fundamental ``magnon'' excitations which obey a dispersion relation that is periodic in the momentum of the magnons This result for the dispersion relation was also shown to hold at arbitrary 't Hooft coupling Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description The crucial idea is that the momentum is interpreted in the string theory side as a certain geometrical angle We use these results to compute the energy of a spinning string We also show that the symmetries that determine the dispersion relation and that constrain the S-matrix are the same in the gauge theory and the string theory We compute the overall S-matrix at large 't Hooft coupling using the string description and we find that it agrees with an earlier conjecture We also find an infinite number of two magnon bound states at strong coupling, while at weak coupling this number is finite

Singularities of the magnon S matrix

Abstract: We investigate, the analytic structure of the magnon S matrix in the spin-chain description of planar Ν = 4 SUSY Yang-Mills/AdS 5 X S 5 strings. Semiclassical analysis suggests that the exact S matrix must have a large family of poles near the real axis in momentum space. In this article we show that these are double poles corresponding to the exchange of pairs of Bogomol'nyi-Prasad-Sommerfield (BPS) magnons. Their locations in the complex plane are uniquely fixed by the known dispersion relation for the BPS particles. The locations precisely agree with the recent conjecture for the S matrix by Beisert, Hernandez, Lopez, Eden, and Staudacher (J. High Energy Phys. 11 (2006) 070 and J. Stat. Mech. 01 (2007) P021). These poles do not signal the presence of new bound states. In fact, a certain non-BPS localized classical solution, which was thought to give rise to new bound states, can actually decay into a pair of BPS magnons.

Transcendentality and crossing

Abstract: We discuss possible phase factors for the S-matrix of planar gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN scaling, Kotikov?Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd-zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS5 ? S5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.

Holographic c-theorems in arbitrary dimensions

Abstract: We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flow is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

Giant Magnons

Abstract: Studies of ${\cal N}=4$ super Yang Mills operators with large R-charge have shown that, in the planar limit, the problem of computing their dimensions can be viewed as a certain spin chain These spin chains have fundamental ``magnon'' excitations which obey a dispersion relation that is periodic in the momentum of the magnons This result for the dispersion relation was also shown to hold at arbitrary 't Hooft coupling Here we identify these magnons on the string theory side and we show how to reconcile a periodic dispersion relation with the continuum worldsheet description The crucial idea is that the momentum is interpreted in the string theory side as a certain geometrical angle We use these results to compute the energy of a spinning string We also show that the symmetries that determine the dispersion relation and that constrain the S-matrix are the same in the gauge theory and the string theory We compute the overall S-matrix at large 't Hooft coupling using the string description and we find that it agrees with an earlier conjecture We also find an infinite number of two magnon bound states at strong coupling, while at weak coupling this number is finite

Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory: TBA and excited states

Abstract: Using the thermodynamic Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in Gromov et al. (Integrability for the Full Spectrum of Planar AdS/CFT. arXiv:0901.3753 [hep-th]) for the spectrum of all operators in planar N = 4 SYM theory follows from these equations. In particular, we present the integral TBA type equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analog of DHM formula for the dressing kernel in the mirror kinematics.

On graviton non-gaussianities during inflation

Abstract: We consider the most general three point function for gravitational waves produced during a period of exactly de Sitter expansion. The de Sitter isometries constrain the possible shapes to only three: two preserving parity and one violating parity. These isometries imply that these correlation functions should be conformal invariant. One of the shapes is produced by the ordinary gravity action. The other shape is produced by a higher derivative correction and could be as large as the gravity contribution. The parity violating shape does not contribute to the bispectrum (1, 2), even though it is present in the wavefunction. We also introduce a spinor helicity formalism to describe de Sitter gravitational waves with circular polarization. These results also apply to correlation functions in Anti-de Sitter space. They also describe the general form of stress tensor correlation functions, in momentum space, in a three dimensional conformal field theory. Here all three shapes can arise, including the parity violating one.