Air conditioning for purposes of cooling a unit is an amenity rather than a legal requirement (i.e. a functioning heating unit). If the unit was advertised as having air conditioning then the lack of working air conditioning would be a breach of the rental agreement but I would not use this to justify non-payment of rent. Review the attached link.
This is not a substitute for a consultation with a housing law attorney in your community.
Though I agree with my colleagues that there is no requirement in CA that a landlord be required to provide AC (though heat is required) some Counties or Cities may require it as a local ordinance. As I do not regularly practice in SB, I am not familiar with those specific local laws.
To be sure, I would contact a local landlord-tenant lawyer to determine what your rights - if any - actually are.
Law Office of Adam Jay Jaffe
124 Lomas Santa Fe Dr, #204
Solana Beach, CA 92075
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