arXiv subjects

Andrei Johansen

Publications and source records attributed to Andrei Johansen.

14 recordsLinked to original sources

arXiv2003

Holomorphic Currents and Duality in N=1 Supersymmetric Theories

Twisted supersymmetric theories on a product of two Riemann surfaces possess non-local holomorphic currents in a BRST cohomology. The holomorphic currents act as vector fields on the chiral ring. The OPE's of these currents are invariant under the renormalization group flow up to BRST-exact terms. In the context of electric-magnetic duality, the algebra generated by the holomorphic currents in the electric theory is isomorphic to the one on the magnetic side. For the currents corresponding to global symmetries this isomorphism follows from 't Hooft anomaly matching conditions. The isomorphism between OPE's of the currents corresponding to non-linear transformations of fields of matter imposes non-trivial conditions on the duality map of chiral ring. We consider in detail the $SU(N_c)$ SQCD with matter in fundamental and adjoint representations, and find agreement with the duality map proposed by Kutasov, Schwimmer and Seiberg.

hep-th↗

arXiv1998

Large N limit of orbifold field theories

We consider certain orbifoldization of the ${\cal N}=4$ field theories that leads to ${\cal N}=2,1,0$ field theories in 4 dimensions. These theories were recently analyzed using the string theory perturbation technique. It was found that in the large $N$ limit all correlation functions of the orbifold theories coincide with those of ${\cal N}=4$, modulo the rescaling of the gauge coupling constant. In this paper we repeat the same analysis using the field theoretical language.

hep-th↗

arXiv1996

Colliding Singularities in F-theory and Phase Transitions

We study F-theory on elliptic threefold Calabi-Yau near colliding singularities. We demonstrate that resolutions of those singularities generically correspond to transitions to phases characterized by new tensor multiplets and enhanced gauge symmetry. These are governed by the dynamics of tensionless strings. We also find new transition points which are associated with several small instantons simultaneously shrinking to zero size.

hep-th↗

arXiv1996

A ${\bf Z}_2$ Classification for 2D Fermion Level Crossing

We demonstrate that the number of fermionic zero modes of the static $2$-dimensional Dirac operator in the background of $SU(2)$ static gauge-Higgs field configurations is a topological invariant modulo four. Static configurations which are everywhere odd under parity with even-parity pure gauge behaviour at infinity admit $4n$, $n\in {\bf Z},$ zero modes of the Jackiw-Rebbi (JR) type. Odd-parity configurations with odd-parity pure gauge behaviour at infinity are topologically disconnected from the vacuum and admit $4 n + 2$ fermionic zero energy solutions. The classification implies the collapse of half of the fermion zero modes upon embedding a $2$-dimensional gauge-Higgs configuration (string) with odd-parity pure gauge behaviour at infinity into the $3$-dimensional Minkowski space.

hep-ph↗

arXiv1996

Baryon Number Non-Conservation and the Topology of Gauge Fields

An introduction to the subject of baryon number non-conservation in the electroweak theory at high temperatures or energies is followed by a summary of our discovery of an infinite surface of sphaleron-like configurations which play a key role in baryon-number non-conserving transitions in a hot electroweak plasma.

hep-ph↗

arXiv1995

$Z_2$ as the Topological Origin of B+L Violation in the Hot Electroweak Theory

The space of static finite-energy configurations in the electroweak theory admits a $Z_2$ topological structure. More precisely, we show that this space contains two disconnected sectors of unstable gauge-Higgs fields odd under a properly defined generalized parity. This classification extends the description of baryon and lepton number violating electroweak processes to the symmetric phase of the theory. Configurations with odd pure-gauge behaviour at spatial infinity, such as the sphaleron, multisphalerons, electroweak strings as well as an infinite surface of their equivalents, have half-integer Chern-Simons number and mediate B+L violating processes in the early universe. Finite-energy configurations with even pure-gauge behaviour, such as the $S^*$ new sphaleron and electroweak strings, are topologically equivalent to the vacuum and are irrelevant for B+L violation. We discuss the possible formation of B+L violating quark-lepton condensates in the symmetric high-temperature phase of the electroweak theory.

hep-ph↗

arXiv1995

A ${\bf Z}_2$ Origin for B+L Violation in the Hot Electroweak Theory

The space of static finite-energy configurations of the electroweak theory admits a ${\bf Z}_{2}$ topological structure. Odd-parity configurations with odd pure-gauge behavior at spatial infinity (S sphaleron, W-Z strings, multisphalerons) mediate rapid $B+L$ violation in the Early Universe. Configurations with even pure-gauge behavior (S$^{*}$ sphalerons, W-Z strings, multisphalerons) are trivial and topologically equivalent to the vacuum.

hep-ph↗

arXiv1995

A ${\bf Z_2}$ Structure in the Configuration Space of Yang-Mills Theories

We argue for the presence of a ${\bf Z}_2$ topological structure in the space of static gauge-Higgs field configurations of $SU(2n)$ and $SO(2n)$ Yang-Mills theories. We rigorously prove the existence of a ${\bf Z}_2$ homotopy group of mappings from the 2-dim. projective sphere ${\bf R}P^2$ into $SU(2n)/{\bf Z}_2$ and $SO(2n)/{\bf Z}_2$ Lie groups respectively. Consequently the symmetric phase of these theories admits infinite surfaces of odd-parity static and unstable gauge field configurations which divide into two disconnected sectors with integer Chern-Simons numbers $n$ and $n+1/2$ respectively. Such a ${\bf Z}_2$ structure persists in the Higgs phase of the above theories and accounts for the existence of $CS=1/2$ odd-parity saddle point solutions to the field equations which correspond to spontaneous symmetry breaking mass scales.

hep-th↗

arXiv1994

Exact Multiparticle Amplitudes at Threshold in $ϕ^4$ Theories with Softly Broken $O(\infty)$ Symmetry

We consider the problem of multiparticle production at threshold in a $ϕ^4$-theory with an $O(N_1$$+$$N_2)$ symmetry softly broken down to $O(N_1)\times O(N_2)$ by nonequal masses. We derive the set of recurrence relations between the multiparticle amplitudes which sums all relevant diagrams with arbitrary number of loops in the large-$N$ limit with fixed number of produced particles. We transform it into a quantum mechanical problem and show how it can be obtained directly from the operator equations of motion by applying the factorization at large $N$. We find the exact solutions to the problem by using the Gelfand--Diki\uı representation of the diagonal resolvent of the Schrödinger operator. The result coincides with the tree amplitudes while the effect of loops is the renormalization of the coupling constant and masses. The form of the solution is due to the fact that the exact amplitude of the process $2$$\ra$$n$ vanishes at $n$$>$$2$ on mass shell when averaged over the $O(N_{1,2})$-indices of incoming particles. We discuss what dynamical symmetry is behind this property. We also give an exact solution in the large-$N$ limit for the model of the $O(N)$$+$$singlet$ scalar particle with the spontaneous breaking of a reflection symmetry.

hep-ph↗

arXiv1994

Infinite Conformal Algebras in Supersymmetric Theories on Four Manifolds

We study a supersymmetric theory twisted on a Kähler four manifold $M=Σ_1 \times Σ_2 ,$ where $Σ_{1,2}$ are 2D Riemann surfaces. We demonstrate that it possesses a "left-moving" conformal stress tensor on $Σ_1$ ($Σ_2$) in a BRST cohomology, which generates the Virasoro algebra with the conventional commutation relations. The central charge of the Virasoro algebra has a purely geometric origin and is proportional to the Euler characteristic $\c$ of the $Σ_2$ ($Σ_1$) surface. It is shown that this construction can be extended to include a realization of a Kac-Moody algebra in BRST cohomology with a level proportional to the Euler characteristic $\c .$ This structure is shown to be invariant under renormalization group. A representation of the algebra $W_{1+\infty}$ in terms of a free chiral supermultiplet is also given. We discuss the role of instantons and a possible relation between the dynamics of 4D Yang-Mills theories and those of 2D sigma models.

hep-th↗

arXiv1994

Realization of $W_{1+\infty}$ and Virasoro Algebras in Supersymmetric Theories on Four Manifolds

We demonstrate that a supersymmetric theory twisted on a Kähler four manifold $M=Σ_1 \times Σ_2 ,$ where $Σ_{1,2}$ are 2D Riemann surfaces, possesses a "left-moving" conformal stress tensor on $Σ_1$ ($Σ_2$) in the BRST cohomology. The central charge of the Virasoro algebra has a purely geometric origin and is proportional to the Euler characteristic of the $Σ_2$ ($Σ_1$) surface. This structure is shown to be invariant under renormalization group. We also give a representation of the algebra $W_{1+\infty}$ in terms of a free chiral supermultiplet.

hep-th↗

arXiv1994

Topological Classification of Odd-Parity Sphaleron Deformations

We discuss topological aspects of the electroweak sphaleron and its odd-parity deformations. We demonstrate that they are uniquely classified in terms of their odd and even-parity pure gauge field behaviour at spatial infinity. Fermion level crossing occurs only for odd-parity configurations which are topologically disconnected from the vacuum. They contribute to the high temperature unsuppressed baryon violating thermal transitions. Deformations with even-parity pure gauge behaviour at spatial infinity are topologically trivial and do not mediate baryon number violation in the early Universe.

hep-ph↗

arXiv1993

An $O(3)$ Global Anomaly in 0+1 Dimension

We present a simple exactly solvable quantum mechanical example of the global anomaly in an $O(3)$ model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, $π_1 (O(3)) ={\bf Z}_2$, fermionic level crossing or circling occur in the eigenvalue spectrum of the 1-dim. Dirac \op under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate 2-dim. Dirac \op . We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

hep-ph↗

arXiv1993

The Level Crossing Phenomenon with Yukawa Interactions

In the minimal model of electroweak interactions we carefully investigate the spectrum of the massive euclidean \dop \ in three, four and five dimensions ($D$) in the presence of \tly \ nontrivial \exl \ fields. More specifically we study the cases of the \inst \ ($D=4$), \sp \ ($D=3$) as well as that of the ($D=5$) \dop \ that pertains to the existence of the \gl \ $SU(2)$ \an . We establish the \exst \ of \nl \ massive fermion \zm s in all three cases. We give closed form expressions which relate the massive with the massless \zm s. As a consequence the \lc \ phenomenon is shown to be manifest and generic in the presence of Yukawa interactions.

hep-ph↗