Abstract
Ultra strong magnetic field could be there in the interior of neutron stars.Strong magnetic field can also be produced inheavy ion collision experiments. I will discuss chiral symmetry breaking inhot and dense quark matter in presenceof strong magnetic field within a 3 flavor Nambu Jona Lasinio model. Whilemagnetic catalysis of chiral symmetrybreaking is expected for hot matter, inverse magnetic catalysis for chiralsymmetry breaking is expectedat finite chemical potential. The equation of state for strange quark matteris derived within the model. The effect of pressureanisotropy of dense quark matter in presence of magnetic field in the grossstructural properties of neutron stars will also be discussed.
