arXiv subjects

Joseph A. Minahan

Publications and source records attributed to Joseph A. Minahan.

At least 37 records · Page 2Linked to original sources

arXiv2015

Phases of planar 5-dimensional supersymmetric Chern-Simons theory

In this paper we investigate the large-$N$ behavior of 5-dimensional $\mathcal{N}=1$ super Yang-Mills with a level $k$ Chern-Simons term and an adjoint hypermultiplet. As in three-dimensional Chern-Simons theories, one must choose an integration contour to completely define the theory. Using localization, we reduce the path integral to a matrix model with a cubic action and compute its free energy in various scenarios. In the limit of infinite Yang-Mills coupling and for particular choices of the contours, we find that the free-energy scales as $N^{5/2}$ for $U(N)$ gauge groups with large values of the Chern-Simons 't\,Hooft coupling, $\tildeλ\equiv N/k$. If we also set the hypermultiplet mass to zero, then this limit is a superconformal fixed point and the $N^{5/2}$ behavior parallels other fixed points which have known supergravity duals. We also demonstrate that $SU(N)$ gauge groups cannot have this $N^{5/2}$ scaling for their free-energy. At finite Yang-Mills coupling we establish the existence of a third order phase transition where the theory crosses over from the Yang-Mills phase to the Chern-Simons phase. The phase transition exists for any value of $\tildeλ$, although the details differ between small and large values of $\tildeλ$. For pure Chern-Simons theories we present evidence for a chain of phase transitions as $\tildeλ$ is increased. We also find the expectation values for supersymmetric circular Wilson loops in these various scenarios and show that the Chern-Simons term leads to different physical properties for fundamental and anti-fundamental Wilson loops. Different choices of the integration contours also lead to different properties for the loops.

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arXiv2014

Computing Three-Point Functions for Short Operators

We compute the three-point structure constants for short primary operators of N=4 super Yang-Mills theory to leading order in the inverse coupling by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.

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arXiv2013

5D super Yang-Mills theory and the correspondence to AdS$_7$/CFT$_6$

We study the relation between 5D super Yang-Mills theory and the holographic description of 6D (2,0) superconformal theory. We start by clarifying some issues related to the localization of N=1 SYM with matter on $S^5$. We concentrate on the case of a single adjoint hypermultiplet with a mass term and argue that the theory has a symmetry enlargement at mass M=1/(2r), where r is the $S^5$ radius. However, in order to have a well-defined localization locus it is necessary to rotate M onto the imaginary axis, breaking the enlarged symmetry. Based on our prescription, the imaginary mass values are physical and we show how the localized path integral is consistent with earlier results for 5D SYM in flat space. We then compute the free energy and the expectation value for a circular Wilson loop in the large N limit. The Wilson loop calculation shows a mass dependent constant rescaling between weak and strong coupling. The Wilson loop continued back to to the enlarged symmetry point is consistent with a supergravity computation for an M2 brane using the standard identification of the compactification radius and the 5D coupling. If we continue back to the physical regime and use this value of the mass to determine the compactification radius, then we find agreement between the SYM free energy and the corresponding supergravity calculation. We also verify numerically some of our analytic approximations.

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arXiv2012

Holographic three-point functions for short operators

We consider holographic three-point functions for operators dual to short string states at strong coupling in N=4 super Yang-Mills. We treat the states as point-like as they come in from the boundary but as strings in the interaction region in the bulk. The interaction position is determined by saddle point, which is equivalent to conservation of the canonical momentum for the interacting particles, and leads to conservation of their conformal charges. We further show that for large dimensions the rms size of the interaction region is small compared to the radius of curvature of the AdS space, but still large compared to the string Compton wave-length. Hence, one can approximate the string vertex operators as flat-space vertex operators with a definite momentum, which depends on the conformal and R-charges of the operator. We then argue that the string vertex operator dual to a primary operator is chosen by satisfying a twisted version of Q^L=Q^R, up to spurious terms. This leads to a unique choice for a scalar vertex operator with the appropriate charges at the first massive level. We then comment on some features of the corresponding three-point functions, including the application of these results to Konishi operators.

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arXiv2012

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection we present an overview of the achievements and the status of this subject as of the year 2010.

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arXiv2011

Supergraphs and the cubic Leigh-Strassler model

We discuss supergraphs and their relation to "chiral functions" in N=4 Super Yang-Mills. Based on the magnon dispersion relation and an explicit three-loop result of Sieg's we make an all loop conjecture for the rational contributions of certain classes of supergraphs. We then apply superspace techniques to the "cubic" branch of Leigh-Strassler N=1 superconformal theories. We show that there are order 2^L/L single trace operators of length L which have zero anomalous dimensions to all loop order in the planar limit. We then compute the anomalous dimensions for another class of single trace operators we call one-pair states. Using the conjecture we can find a simple expression for the rational part of the anomalous dimension which we argue is valid at least up to and including five-loop order. Based on an explicit computation we can compute the anomalous dimension for these operators to four loops.

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arXiv2011

Review of AdS/CFT Integrability, Chapter I.1: Spin Chains in N=4 Super Yang-Mills

In this chapter of "Review of AdS/CFT Integrability" we introduce N=4 Super Yang-Mills. We discuss the global superalagebra PSU(2,2|4) and its action on gauge invariant operators. We then discuss the computation of the correlators of certain gauge invariant operators, the so-called single trace operators in the large N limit. We show that interactions in the gauge theory lead to mixing of the operators. We compute this mixing at the one-loop level and show that the problem maps to a one-dimensional spin chain with nearest neighbor interactions. For operators in the SU(2) sector we show that the spin chain is the ferromagnetic Heisenberg spin chain whose eigenvalues are determined by the Bethe equations.

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arXiv2006

Strong coupling from the Hubbard model

It was recently observed that the one dimensional half-filled Hubbard model reproduces the known part of the perturbative spectrum of planar N=4 super Yang-Mills in the SU(2) sector. Assuming that this identification is valid beyond perturbation theory, we investigate the behavior of this spectrum as the 't Hooft parameter λbecomes large. We show that the full dimension Δof the Konishi superpartner is the solution of a sixth order polynomial while Δfor a bare dimension 5 operator is the solution of a cubic. In both cases the equations can be solved easily as a series expansion for both small and large λand the equations can be inverted to express λas an explicit function of Δ. We then consider more general operators and show how Δdepends on λin the strong coupling limit. We are also able to distinguish those states in the Hubbard model which correspond to the gauge invariant operators for all values of λ. Finally, we compare our results with known results for strings on AdS_5\times S^5, where we find agreement for a range of R-charges.

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arXiv2005

Higher Loops Beyond the SU(2) Sector

We consider the case of coherent gauge invariant operators in the SU(3) and SO(4) sectors. We argue that in many cases, these sectors can be closed in the thermodynamic limit, even at higher loops. We then use a modification of the Bethe equations which is a natural generalization of a proposal put forward by Serban and Staudacher to make gauge theory predictions for the anomalous dimensions for a certain class of operators in each sector. We show that the predictions are consistent with semiclassical string predictions at two loops but in general fail to agree at three loops. Interestingly, in both cases there is one point in the configuration space where the gauge theory and string theory predictions agree. In the SU(3) case it corresponds to a circular string with R-charge assignment (J,J,J).

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arXiv2005

The SU(2) sector in AdS/CFT

In the large N limit of N=4 Super Yang-Mills, the mixing under dilatations of the SU(2) sector, single trace operators composed of L complex scalar fields of two types, is closed to all orders in perturbation theory. By relying on the AdS/CFT correspondence, and by examining the currents for semiclassical strings, we present evidence which implies that there are small mixings that contradict the closure of the SU(2) sector in the strong coupling limit. These mixings first appear to second order in the λ/L^2 expansion.

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arXiv2004

Circular Semiclassical String Solutions on AdS_5 x S_5

We discuss two semiclassical string solutions on AdS_5\times S_5. In the first case, we consider a multiwrapped circular string pulsating in the radial direction of AdS_5, but fixed to a point on the S_5. We compute the energy of this motion as a function of a large quantum number $n$. We identify the string level with $mn$, where $m$ is the number of string wrappings. Using the AdS/CFT correspondence, we argue that the bare dimension of the corresponding gauge invariant operator is $2n$ and that its anomalous dimension scales as λ^{1/4}\sqrt{mn}, for large $n$. Next we consider a multiwrapped circular string pulsating about two opposite poles of the $S_5$. We compute the energy of this motion as a function of a large quantum number, $n$ where again the string level is given as $mn$. We find that the dimension of the corresponding operator is 2n(1+f(m^2λ/(2n)^2)), where f(x) is computible as a series about x=0 and where it is analytic. We also compare this result to the BMN result for large J operators.

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arXiv2002

Stretched strings in tachyon condensation models

In this note, we consider the two derivative truncation of boundary string field theory for unstable D9 branes in Type IIA string theory. We construct multiples of the stable codimension 1 solitons that correspond to stacks of D8 branes. We find the fluctuation modes that correspond to open strings stretching between the branes, and find that their masses are consistent with the string tension. We show that these modes are localized halfway between the branes and that their width is independent of the brane separation.

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arXiv2002

Rolling the tachyon in super BSFT

We investigate the rolling of the tachyon on the unstable D9 brane in Type IIA string theory by studying the BSFT action. The action is known for linear profiles of the tachyon, which is the expected asymptotic behavior of the tachyon as it approaches the closed string vacuum, as recently described by Sen. We find that the action does indeed seem consistent with the general Sen description, in that it implies a constant energy density with diminishing pressure. However, the details are somewhat different from an effective field theory of Born-Infeld type. For instance, the BSFT action implies there are poles for certain rolling velocities, while a Born-Infeld action would have a cut. We also find that solutions with pressure diminishing from either the positive or negative side are possible.

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arXiv2001

Quantum Corrections in p-adic String Theory

We compute loop corrections in p-adic open string field theory. We argue that quantum effects induce a pole with m^2 ~ - ln g for the open string field at the locally stable vacuum. We also compute the one loop effective potential and show that the potential develops an imaginary piece when the field becomes tachyonic.

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arXiv2001

Mode Interactions of the Tachyon Condensate in p-adic String Theory

We study the fluctuation modes for lump solutions of the tachyon effective potential in p-adic open string theory. We find a discrete spectrum with equally spaced mass squared levels. We also find that the interactions derived from this field theory are consistent with p-adic string amplitudes for excited string states.

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arXiv2000

Gauge Fields and Fermions in Tachyon Effective Field Theories

In this paper we incorporate gauge fields into the tachyon field theory models for unstable D-branes in bosonic and in Type II string theories. The chosen couplings yield massless gauge fields and an infinite set of equally spaced massive gauge fields on codimension one branes. A lack of a continuum spectrum is taken as evidence that the stable tachyon vacuum does not support conventional gauge excitations. For the bosonic string model we find two possible solvable couplings, one closely related to Born-Infeld forms and the other allowing a detailed comparison to the open string modes on bosonic D-branes. We also show how to include fermions in the type II model. They localize correctly on stable codimension one branes resulting in bose-fermi degeneracy at the massless level. Finally, we establish the solvability of a large class of models that include kinetic terms with more than two derivatives.

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arXiv2000

Effective Tachyon Dynamics in Superstring Theory

A recently proposed \ell=\infty field theory model of tachyon dynamics for unstable bosonic D-branes has been shown to arise as the two-derivative truncation of (boundary)-string field theory. Using an \ell\to \infty limit appropriate to stable kinks we obtain a model for the tachyon dynamics on unstable D-branes or D-brane anti-D-brane pairs of superstring theory. The tachyon potential is a positive definite even function of the tachyon, and at the stable global minima there is no on-shell dynamics. The kink solution mimics nicely the properties of stable D-branes: the spectrum of the kink consists of infinite levels starting at zero mass, with spacing double the value of the tachyon mass-squared. It is natural to expect that this model will arise in (boundary) superstring field theory.

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arXiv2000

Field theory models for tachyon and gauge field string dynamics

In hep-th/0008227, the unstable lump solution of ϕ^3 theory was shown to have a spectrum governed by the solvable Schroedinger equation with the \ell=3 reflectionless potential and was used as a model for tachyon condensation in string theory. In this paper we study in detail an \ell\to \infty scalar field theory model whose lump solution mimics remarkably the string theory setup: the original field theory tachyon and the lump tachyon have the same mass, the spectrum of the lump consists of equally spaced infinite levels, there is no continuous spectrum, and nothing survives after tachyon condensation. We also find exact solutions for lumps with codimension \ge 2, and show that that their tensions satisfy (1/(2π)) (T_p/ T_{p+1})=e/(\sqrt{2π}) \approx 1.08. We incorporate gauge fixed couplings to a U(1) gauge field which preserve solvability and result in massless gauge fields on the lump.

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