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Welcome to the site.
I am sorry to learn about your predicament and i empathise with you.
You see if he has been actively taking alcohol and if this affair has started as a result of his impaired judgment owing to alcohol abuse then it is quite likely that he may come back to you once he starts getting sober all over again and subsequently regains his insight and judgment which will help him to realise his fault and force him to contact you. However, if he continues to drink the way he has been off late then no one can predict when he is going to come out of this trip of his. So, it is a precarious situation to say the least owing to his alcohol addiction, so with all honesty I would say that you shall give yourself a realistic time frame of weeks or months so as to wait for his return and if that does not happen then you should try to get past this relationship which will be difficult no doubt, but it will be the best decision for you at that time, since life has to move on, it cannot remain static for anyone. If he chooses not to return for the sake of this relationship then you should honor your self esteem and try to break these shackles of relationship and start thinking